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6r "/«**■ 
 
 V*' /Report No. UIUCDCS-R-77-907 
 
 MULTIPROCESSOR FOR STRING MANIPULATION 
 
 UILU-ENG 77 176^ 
 
 by 
 Wing Kai Cheng 
 
 October 1977 
 
 NSF-OCA-MCS73-07980-000029 
 
Digitized by the Internet Archive 
 in 2013 
 
 http://archive.org/details/multiprocessorfo907chen 
 
Report No. UIUCDCS-R-77-907 
 
 MULTIPROCESSOR FOR STRING MANIPULATION* 
 
 by 
 Wing Kai Cheng 
 
 October 1977 
 
 Department of Computer Science 
 
 University of Illinois at Urbana-Champaign 
 
 Urbana, Illinois 61801 
 
 This work was supported in part by the National Science Foundation under 
 Grant No. US NSF-MCS73-07980 and was submitted in partial fulfillment of 
 the requirements for the degree of Master of Science in Computer Science, 
 October 1977. 
 
iii 
 
 ACKNOWLEDGEMENT 
 
 I would like to thank my advisor Professor David J. 
 Kuck for Jus advice, guidance, incisive questions, 
 encouragement, and general concern. 
 
 Many others also deserve much thanks — a partial list 
 includes Professor R. P. Futrelle, mv friends, and my 
 naren ts. 
 
1 V 
 
 TABLE UF CONTENTS 
 
 PAGE 
 
 INTRODUCTION I 
 
 AN OVERVI f:rf OF SNOROI 4 
 
 2. I Introduct ion 4 
 
 2.2 Syntax and Semantics b 
 
 2.3 Serial Execution 1 I 
 
 2.3.1 Pronram Execution II 
 
 2.3.2 5 tat orient F/xectuion 11 
 
 2.3.3 Sari al Pattern Matching 13 
 
 2.4 Sp ^e dup 16 
 
 2.4.1 Speeduo of the. Has ic Operations 16 
 
 2.4.2 -So aadup at Statement Leve 1 1 / 
 
 2.4.3 Speedup in the Proqram Laval 1/ 
 
 2.4.4 IF Tr fie 1 ci 
 
 PATTERNS AIL) PATTERN MATCHING PROCESSOR 22 
 
 3. 1 Introduction 22 
 
 3.2 Algebra of Pattern Matching 22 
 
 3.2.1 Deviation from SNOBOL4 23 
 
 3.3 i'ime Bound for Pattern Matching Algorithm 
 
 i n SN0BGL4 29 
 
 3.4 Pattern Matchinn Network 31 
 
3.4.1 Staae I 3/ 
 
 3.4.1.1 Comparison of the Methods 40 
 
 3.4.2 Design of Stage I 41 
 
 3.4.2. I Speed 50 
 
 3.4.3 Stage II 50 
 
 3.4.4 Stage III 50 
 
 3 . 4 . 5 : , t age IV 51 
 
 3.4.6 Stage V 51 
 
 3.4./ : ; t age via 51 
 
 3 . 4 . .i St ane VI b 52 
 
 3. 5 Catn , Time, and liate* f i mo 52 
 
 MACHINE DES-JCU 66 
 
 4 . I [1 vera 11 Organ i z at ion . ^6 
 
 A . 2 Oarbane Co llect ion . . 67 
 
 4 . 3 I K- Tr ee Processor 69 
 
 4. 1 Memory 70 
 
 A . 5 Proqram Memory 72 
 
 4.6 Data Memory.. 72 
 
 4.7 Instruction Set , 7/ 
 
 i-:;ipi RICAL results ul 
 
 5.1 I ntroduct ion 31 
 
 5.2 Stacic Frequency Count 32 
 
vi 
 
 13.3 Ovnamic Statistics 37 
 
 6. SYSTEM PARAMETERS 88 
 
 6. I Introduct ion 83 
 
 6.2 Descriptor Size 3d 
 
 6 . 3 Descri ntor Forma t 88 
 
 6. 4 Character Size 89 
 
 6. 2 M,U Processor 90 
 
 6.6 IF Free Processor 9 1 
 
 6.7 Pro or am Memory 9 1 
 
 6. 8 Data Memory 92 
 
 6.9 PMM , 93 
 
 6 . 10 Ex o e c 1*. ed S p eed w p 94 
 
 7. GUNCLUSIOM 96 
 
 FIST HF REFERENCES 97 
 
I. INTRODUCTION 
 
 In the past decade, there has been significant 
 improvement in computer speed as a result of faster and 
 faster gates, and computer organization which exploits 
 parallel processing. This treni is expected to continue, 
 with major improvement to come from computer organization, 
 as switching speed is approaching its theoretical limit, and 
 the declining cost and the progress of LSI technology are 
 making the exploitation of parallelism economically and 
 physically possible. It is this computer organization 
 (machine and software) aspect which this thesis is concerne I 
 with. 
 
 Many proposals and attempts have been made to soeed-uo 
 the execution of numerical nroblpms on computers, and eech 
 has achieved some form of success. In some cas^s, actual 
 machines have bpen built or are being built: some .examples 
 of which are ILLUC IV. CRAY I, CDC 7700, COC STAR, II ASC, 
 etc. 
 
 ("In the other hand, computer organization lor 
 
non-numerical computing is still in its infancv, although 
 there are orobably mor^ non-numerical oroblems than 
 numerical ones in this world. f tie fpllowina result is 
 probably familiar to many people [GIM76J: To multiply two 3 
 dioits numbers, it takes the computer 6 microseconds as 
 compared to about 60 seconds by human — the computer is 
 therefore 10**/ Limes fester than human. To search for a 
 ten character strinn in a 3000 characters text takes a 
 typical computer 6 milliseconds, whereas it takes a human 
 being 60 seconds — thus the machine is 10**4 times faster 
 then human. Comoarinq the two situations, one may conclude 
 
 that the machine is about 10**3 times faster with numerical 
 oroblems than it is with non-numerical oroblems. The 
 obvious reason for this inefficiency for non-numerical 
 problems is that non-numerical oroblems and lanquacjes 
 contain facilities and concepts so far removed from t lie 
 conventional machines that elaborate software is required to 
 bridge toe man. Furthermore, parallelism and functional 
 requirements are not as well understood and exploited in 
 machines for these non-numerical problems as they are for 
 tlie numerical counterparts. 
 
With t lie increasinq usaqe of comnuters for 
 
 non-numerical data process inn, it has become innro i moor tent 
 to process this kind of data more efficiently and faster. 
 The primary objective of this research is to studv the 
 requirements and peculiarities of strinn orocessinn, and to 
 propose a machine organization that is suitable for strinn 
 orocessinn in terms of speed and ease of sunportinq software 
 features of their lnnquaqes. A well known strinn orocessinn 
 lanouane called SNOBOLI PCM 7 i ] will be used as a 
 r eoresen ta ti ve strinn process inn lannuane for our studv. 
 
 ;.'e start off with Chapter 2 as a svnopsis of the basic 
 features of o'KJBUL, and an introduction to our aoproach of 
 speedino up SNGBDL. Alqebraic properties of natterns and 
 the design of a oattern matchinn network are presented in 
 chapter J. The machine ornani zat ion and its instruction set 
 are described in Chapter 4. Gome emoirical results of 
 SNUDQL nronrams are given in Chapter 5. Chanter n discusses 
 the system oarameters and nives an estimation of the sneeduo 
 achievable. Conclusions and sunocstions for further 
 research can be found in Chapter /. 
 
2. AN OVERVIEW OF SMGBUL 
 2 . 1 In troduct ion 
 
 3NUBUL is mainly a lanouane for strino: manipulation, 
 containing many features not readily found in other 
 proqrarnminrj languages. i'his language oroves to be a 
 useful tool in areas such as compilation, machine 
 simulations, symbolic mathematics, text preparation, 
 natural language translation, linguistics, music analysis, 
 information retrieval, artificial intelligence research, 
 and tne like. i'ue fart that it is implemented in several 
 different computers (includinn I MM System /360 and 370, 
 UNIVAC I 109, GE63 C 3, CDC 3600, CDC 6000 series, P0P10, 
 Sigma 15/6/7, Atlas 2, and RCA Spectra Series) nrobably 
 reflects t fie wide acceptance bv the users. 
 
 i'he basic operations in SIJOBOL, in addition to t ne 
 usual arithmetic and assignments, include concatenation. 
 alternation , and pattern m ate iiina . i'ne basic data element 
 of SfJUBOL is the strino, that is, a strino of characters. 
 INUliUL also provides numerical capabilities witn both 
 interjers and real numbers, and automatic conversion 
 
13 
 
 capability between string and numerical values. Intener 
 is more often used than real number because most numerical 
 operations involve character count inn. 
 
 Structured data types include those of arrays, which 
 can be accessed through index, and tables, which can be 
 accessed through variables. 
 
 2.2 Syntax ami Semantics 
 
 A brief description of the SNQBOL syntax and 
 semantics is provided in this section in order to ooint 
 out some of the peculiarities and properties of SNOBDL and 
 Highlight features we propose for sneeduo. A more 
 detailed and complete description of SNDRDL can be found 
 in [PDA /I ,Uf?I /2J. 
 
 i'he syntax of SNUBOL will be defined bv the 
 traditional Backus-Naur form [ BACb9, NAU63J , where 
 syntactic constructs are denoted by English words in lower 
 case letters. Sequences of constructs separated by t ho 
 meta-symbols { and ) imnly t ho i r repetition zero or more 
 
times. In addition, we choose to use '::=' to separate 
 left part of the production from the possible rioht parts. 
 
 The notation [x3 ".'ill be used to indicate that the? term k 
 
 is optional. 
 
PRODUCTION RULES 
 
 COMMENT 
 
 program ::={[ label J statement) 
 
 END Ccharacter-stringJ 
 
 label : :=character string 
 
 statement: : =[ rule ] 
 
 : i 
 
 s=rule 
 
 • 
 • 
 
 qoto 
 
 
 • i 
 
 • 
 
 :=rule 
 
 : 
 
 S goto 
 
 
 • 
 • 
 
 t=rule 
 
 : 
 
 S qotol 
 
 F goto2 
 
 : : 
 
 '=rule 
 
 • 
 
 F goto 
 
 
 : i 
 
 !=rule 
 
 • 
 • 
 
 F gotol 
 
 S qoto2 
 
 goto: : =( exor ) 
 
 
 
 
 : : = 
 
 <expr> 
 
 
 
 
 rule 
 
 [expr] 
 exor = 
 
 ; exprl = expr2 
 exorl expr2 
 ; exnr 1 exnr2 = 
 : exor I exor2 = exor3 
 
 no qoto 
 
 unconditional qoto 
 S qoto 
 
 S-F qoto 
 F qotO 
 
 F-S qoto 
 
 normal qoto 
 direct qoto 
 
 f j xnression evaluation 
 null assignment 
 ass ignment 
 oattern match 
 null reolacement 
 string reolacement 
 
 expr 
 
 ^'character-string' 
 :=number 
 :=ident i f i er 
 :=operator expr 
 :=exorl ooerator expr2 
 :=identifier ((expr)) 
 :=identifier <<expr}> 
 
 1 it era 1 
 number 
 identifier 
 unary ooeration 
 binary operation 
 function call 
 array indexing 
 
 Table 2.2-1 Simplified SNOBOL Syntax 
 
A SNUBUL nroqram consists of a sequence of statements 
 
 which ara executed sequentially unless control is 
 transferred elsewnere. \ statement, as shown in Table 
 
 2.2-1, contains up to two oarts: rule and qoto. The 
 
 execution of a statement merely determines which statement 
 
 is to be evaluated next; in other words, the statement 
 
 itself carries with it no value and does not succeed or 
 
 fail. .Jithin a statement, mila. is evaluated first, and 
 
 its success or failure is used to influence the qoto nart 
 
 to determine the subsequent statement to be evaluated. If 
 
 the statement is without a qoto, the subsequent statement 
 
 is evaluated; however, if the statement is with a 
 
 conditional qoto, control is transferred to the statement 
 
 indicated by the evaluation of the ooto, S qoto or F qoto 
 
 is evaluated when the rule si qnals success or failure 
 
 respectively. If th^ rule siqnals success (failure) and 
 
 the statement is without S qoto (F nolo), control is 
 
 simply transferred to the followinq statement in the 
 
 program. 
 
 Tne three main classes of statements are 
 
 ( I ) ass iqnment , (2)nattcrn matchino, and ( 3)replacement , 
 
depending on the rule part. 
 
 As sixjwn in Table 2.2-1, assignment has the form 
 sub iect = o b iect 
 
 Pattern matching takes the General form 
 
 s_uli.L2.ci etattern 
 wnereby during execution, subj ect is inspected for the 
 
 occurrence of pattern. 
 
 The replacement statement is a combination of oattern 
 mate hi nq and as si on merit, in which the matched strino is 
 reolaced by the string in the object field. [ i^. form is 
 
 subject aait.ern = obj 
 
 The result of the execution of the r ul e is either a 
 success or failure. If the evaluation of any one of exor, 
 expr 1 , expr2 , or expr3 should fail, then no further parts 
 of the rule are evaluated, and the' whole rule fails. More 
 specifically, if the rule is an expression (exnr) 
 evaluation, null assignment, or assignment, the rule 
 succeeds if none of the exor fails. 
 
10 
 
 In pattern matchinci, oxnrl and then exnr? are 
 evaluated and coerced. i : xor1 is then used as t lie ?\ih ject 
 or text . and expr2 is used as the na ttern . Pattern 
 matching either succeeds or fails. 
 
 In the case of t he nattern match rep lac anient , axprl 
 and exor2 are evaluated as in pattern match. If the match 
 succeeds, exnr3 renlaces the matched substring I hroug h t ne 
 use of concatenations. If exnr.3 is missing from the rule, 
 exnr3 is assumed to be a null string. 
 
 i"he evaluation of an expression may either succeed or 
 fail. If evaluation succeeds, the result may either be 
 returne d ov n a a e (when the result of the evaluation is a 
 location) or retu rned by YclilUl (when the result is a 
 storable value). If the evaluation fails, it is known as 
 fail ret urn . If a location is returned by name when a 
 value is needed in an operation, the ooeration may 
 retrieve the value associated with the location? this 
 nrocess of retrieval for value when a location is returned 
 is known as c oerc ion. 
 
Execution 
 
 The order of execution in a serial SNOBOL prooran i 55 
 presented in this section. 
 
 2.3.1, Iirj2.or.ajn Ex.s.c.iit.ijQQ 
 
 As notfd earlier, statements in a SMGRUL. nronram are 
 executed in a sequential order unless control is 
 transferred elsewnere by a qoto. Transfer of control can 
 be either unconditional or conditional, as in other 
 programming lanquanes. 
 
 2,3.2 S ta bernent tl xecut ion 
 
 A SNUI3DL statement, having the general form 
 
 subject pattern = object ooto is evaluated in a 
 sequential order as follows [PDA/]]: 
 
 I. The subject is evaluated first. If t ne 
 evaluation fails, t lie statement fails, noto is 
 evaluated, and the other components of the statement 
 are not evaluated. If no failure goto is specified, 
 
control is passed to the next statement. 
 
 2. Fhe pattern is then evaluated. If the evaluation 
 fails, qoto is evaluated as in the case of subject 
 failure in ( I ) . 
 
 3. fhe pattern natch is performed next. If the 
 match fails, the .statement fails, conditional value 
 
 assignment is not perf orrned, the replacement is 
 skipped, and the noto is processed. Immediate value 
 
 assignments may take place before the pattern match 
 
 fails. If oattern matching succeeds, conditional 
 
 value assignment is performed for those components 
 
 that matcned. 
 
 4. fhe object is evaluated. If evaluation fails, 
 the statement fails, no replacement is performed, and 
 the goto is processed. 
 
 b. The replacement is performed. 
 
 6. fhe no to is processed. The three possibilities 
 
 ar e : 
 
 (a) If the statement succeeds, onlv an 
 unconditional or success goto in the statement 
 
 i s processed. 
 
IJ 
 
 (b) If the statement fails, only an 
 unconditional goto or failure goto in the 
 sta Lenient is evaluated. 
 
 (c) Transfer is made to an evaluated goto, if 
 there is one. 
 
 If none of the three conditions above is met, control 
 is transferred to the next statement. 
 
 2.3.3 S eria l Pa tter n Match ing 
 
 Pattern mate hi no can be a very time consuming 
 process, as illustrated by the following example. 
 
 Consider a pattern of the form 
 ST = CH'I'BRE') CH'I'A') '0' 
 which has three subsequents to the right of the pqualitv 
 sign, where the first and second has two alternates each. 
 '!' is used to denote alternation, the soaces between 
 CIJ'I'BRE') and CE'S'A') and that between Ch'l'A') and 
 / U / are concatenation ooerators. 
 
14 
 
 The process of pattern matchinn for th.p> pattern ST, 
 
 which matches anv of the string in the set 
 
 D.[3AU,B'?EI£D, BREAD) is shown in big. 2.3.3-1. The 
 
 matching algorithm for SN0RDL4 tPO/V'/l ,3RI72] may be 
 
 s ummar i zjsci as folio ws : 
 
 I. Matching starts with the first alternate of the 
 
 A. i'inen a component matches, the next subsequent to 
 the r in nt is attempted; otherwise, onto (4). 
 
 3. If a match can be obtained for a series of 
 components lead inn from the left through the right, 
 t.ic pattern match is successful. 
 
 4. If a component does not match, an alternate 
 witnin this subsequent is tried. If no alternate 
 exists, the matching process backs up, rejecting the 
 previously matched component and seeks an alternate 
 for it. 
 
15 
 
 ->'U' 'E' 'D' ->'H'->'E' 'V)' 
 
 'BRE' 'A' 'BRE' 'A' 
 
 (a)match for B (b) attempt to match RE, but 
 
 fail 
 
 ->'U'- 'E' '0' '13' 'E' 'D' 
 
 i 
 
 i 
 
 'BRE' ->'A' ->'IMI' 'A' 
 
 (c)attempt to natch BA ( d)backuo , match for BRE 
 but fail 
 
 ->'Bil£'- 'A 7 ->'BRE'->'A' 
 
 (e)attempt to match BREE (f)match for BREA 
 but fail 
 
 subject strinq: BREAD 
 
 pattern: CB'I'BRE') CE'!'//) 'D' 
 
 Fig. 2.3.3-1 Snapshots of a pattern matchinn process in 
 
 SN0B0L4 
 
16 
 
 2.4 Spcsdiia. 
 
 fhe speedup proposed will be a combination of special 
 r Iware and algorithms. Usually, for a given programming 
 language, one can expect that parallelism may be exploited 
 in three different levels: (1) In basic numerical and 
 non-numerical operations, (?) statement level, and (3) 
 program level. All these methods will be explored in more 
 detail in the following sections. 
 
 2.4. i &>eodua o_£ kaa Basic Qp_e rations 
 
 Speedup of the basic numerical operations, such as 
 addition of two numbers or multiplication of two numbers, 
 has been investigated by many people, such as 
 [UAD65,MSn61 J . 
 
 In the next chapter, we shall orooose a way to 
 speedup pattern matching. Speedup of cone itenat i on and 
 alternation can be expected to come mainly from memory 
 bandwidth. 
 
I / 
 
 2.4.2 Unsmdup al ^itatemonL Level 
 
 To speedup at the statement level is to execute as 
 many of the cornnon<~ , nts of a statement in narallel as 
 possible. For a numerical statement, it is to evaluate 
 the numerical expression through multiprocessing 
 [MUR71 ,KRA72,[<UC7?J . 
 
 For example, to evaluate 
 a=b+c +d+e , 
 
 one needs a minimum time of two adder delays, using thr^e 
 adders. In general, to evaluate an expression consisting 
 of n terms requires |log2 n) time delay and n-l processors. 
 An analoo to arithmetic expression in strino processing is 
 to perform a pattern matching involving concatenations and 
 alternations; sneeduo of this is discussed in a later 
 chapter. 
 
 2.4.3 £p_e_cjim2 la tlis. Er.Qar.aiii L ova l 
 
 Speedup in the program level involves the execution 
 of more than one statements, at one time. Transformations 
 
of the nronram ?ire requ i. red to remove data denpndency of 
 the statements [i'Llrr/63. An example of these 
 transformations is forward substitution. L"ne statements 
 
 a = c I 
 
 b = a c e 
 
 f = bg 
 can b^ transformed into 
 
 l = c d 
 
 b = c el c e 
 
 f = c d c c n 
 after forward substitution. Interdeoendencics are removed 
 in tne transformed statements: thus, all three statements 
 n r r) executable in oarallel. Care must b« taken to insure 
 that the variables refer to the same value before forward 
 substitution i. r ; performed, since tnis process is 
 complicated bv the fact that SNOimr.. allows inout 
 association, immediate value assignment, and conditional 
 
 va ] ue ass i nnrnent . 
 2.4.4 LL Tree 
 
 In IL, let us refer to the statements "/it 
 
19 
 
 S-qoto, F-goto, 5-F-qoto as decision statements, and 
 collectively call the other tvpe of statements the 
 assinnment statements. 
 
 In a proqram, assinnment statements arp interspersed 
 with decision statements. The oarts of a oroqram where 
 the ratio of decision statements to assinnment statement 
 operations is lamer than an experimentally determined 
 threshold are called IF trees. A decision tree is formed 
 when the assiqnment statements are removed from the IF 
 tree. 
 
 l'o speeduo the execution of a proqram havinn a 
 Significant number of decision statements, an IF tr^e 
 processor may he used. The idea behind the IF tree 
 processor [l)AV72b] is to execute all possible patns and 
 then pick the right results. In order to do this, the 
 followinq steps have to be performed at comoilc time: 
 
 I. A new assiqnment statement, the left hand side of 
 which is a loqical variable is added to each decision 
 statement. These new statements will store the 
 results (success or. failure) of the decision 
 
20 
 
 statements. .Jo will later refer to the values of 
 these logical variables as Si ; values. 
 
 2. Move all the decision statements plus the 
 statements they depend on, to a position ahead of the 
 decision bree; coll these Il-PS. ; iovo the rest of the 
 statements below the tree. Mote that the statements 
 have to ho tanned before tor movement so as to 
 i len t i f v 1 1 e i r pos i t i oris in the I F t r ee . 
 
 3. Map too nodes from the decision tree to th^ 
 processor . 
 
 Uurinn the execution phase. 
 
 1. All statements ahead of the tree are evaluated as 
 fast as possible. 
 
 2. 1'he 5F values that are needed for the decision 
 are given to the IF tree processor. 
 
 3. Evaluate the trep in the IF tree processor and 
 find the orooer oath. 
 
 4. Rased on the path obtained in Stop 3, the nronor 
 results from toe Ii-'Rii are selected, and the 
 statements which had been moved down in compile time 
 
21 
 
 and which are in the selected path are evaluated. 
 
 The rest of the algorithms for IF-tree and its hardware 
 desiqn are similar to that prooosed by Davis [DAV7?b]. 
 
22 
 
 3. PATTERNS Ail!) PATTLittN MATCHING PNUCESSm 
 3. I LnuroJiLclLLon 
 
 Line of the main features and a time consunino process 
 of SiJllDOL i 55 onttorn matcninn. In tnis chanter, wn will 
 discuss the alaebra of pattern matching, some oattern 
 match: no sc nemos, and the tins inn of n nattern matcninci 
 processor. 
 
 3.,! Algebra qX liailani Ia.Lc.iuaa 
 
 Consider the set of characters, consistinn of 
 letters, dinits, punctuation symbols, null character, 
 fi:( character which does not natch anythinq), and ALL 
 (character which matches nn'' character). /Je define n 
 s tr J n .i as =i se )uence of one or more characters. Clearly, 
 a sequence of null characters is called a null strino. 
 
 Let us lenotc the lenath of n string n by !si. \W 
 definition, the Lennth of a null strinn i ". considered to 
 be zero. 
 
23 
 
 If C Is a character sot and a£C, thon n%5 nr 5%a is 
 aqain a string, of length ! s ! + 1 , wnere the symbol / "o / in 
 used to denote the concatenation operator (instead of a 
 space as in SNUBDL) for the sake of clarity* except in 
 places where SNUI30L examples are used. Uith these 
 definitions earned upon, we can try to summarize the 
 nrooerLies of oattern matching that we will use later. 
 Previous work in Luis area of the formalization of nattorn 
 matching had been done by Gimoelt uIM731 , and Stewart 
 [STE74] . 
 
 Pattern matchinci can bo loosely defined as the 
 process of examining the occurrences of a set of 
 substrings called patterns within a lonoer string called 
 subject string. The set of patterns can be expressed with 
 strings, concatenation operators, and alternation 
 operators. A pattern without any concatenation or 
 alternation ooerator (that is, consist inn of a simple 
 strino) is referred to as a si nolo pattern. 
 
 Def Pattern matching is a function h(s,p,c) where s is a 
 string called the subject strino or text, p is a strinp 
 
24 
 
 called the pattern, and c, called t he ore-cursor position, 
 is a pointer to s, tnkinn nn the values in the range 
 I , . . . , I s i-l ol +1 . Thn value or i4(s,p,c) is an integer, 
 called the >ost-cursor oosition, oointinn to the text 
 v/here the match benins. iin can extend Lh^ fefinition a 
 little further to define a oattern matching <v hi c ii finds 
 nil the matches as 
 
 AM(p,5,c)-U M(o,s,c) 
 for all c, where J denotes set union. 
 
 Ii tne post-cursor tak?s on a value outside the niven 
 ranoe of 1 , . . . ! s I -In ! ■» I , the match is considered to have 
 failed. i'ne oattorns HAIL and NULL in SNUHOL can he 
 formally defined as follows! 
 
 Dcf f-'AIL is a oattern defined by 
 
 M(s,i-AIL,c) =d 
 flote that M(s,HAIL,0)~.0. 
 
 Uef MULL is n oattern definei by 
 l .l(s,NULL,c)=c 
 
2 '5 
 t-xample 
 If p=CA r 3 and s=ABACAP>A, and c=0, then M(s,o,c)=4. 
 
 Una can think of an invorso of a oittorn n, as a 
 pattern which doesn't match n. As nn example, the oattrcrn 
 in SflUBDL which matches any character oxc^nt thn character 
 'A, ' wrJ tton in SMQBDL as 
 'A' ADDTi' 
 
 In qeneral, a oattern v/hich matches II but not A is written 
 
 pat = a A r AJ;?'j" : n 
 
 Two patterns PI and P2 are equal iff 
 
 M(s f PI,c)=M(s,P2,c) for all s and c, or 
 
 Ai'.;(s,Pl ,c)=A;'(s, [>:•', c). 
 
 Uc-f The concatenation of P and 0, r^nrnsnntnd h^r^ as P?;'0, 
 whore P and are strinqs, is defined as 
 
 M ( s , P';:d ,c)4i(s,P,c)/)[ M ( s , , c ) - ! i > ; 1 
 
 and in Lho case for all matches 
 
 AM( s , P%Q f c )-AM( s , P, c )f) .C AM (s ,0, c )- In ! ] . 
 
An alternation is an operation which ns.sinn morn than 
 onn strina to a variable; it can be defined in the 
 following manner. 
 
 I)ol : The alternation of P and Q, represented as P!0, is 
 definecJ as tf (s,PJ\), c)=M.(s,P,c ) U M(s,Q,c) and 
 
 Ai.;{.'.;,! ) !0,c)=.U(s,P,c) U A" (s,n,c), where U denotes 
 the set union. 
 
 It is easy to show that the following nrooorties hold 
 under the operations of concatenation end alternation 'live 
 P and Q are patterns? thus, the nronartias are List ' 
 without proof. 
 
 Let P be the set of patterns 
 
 PI. p is closed under alternation. If pfP and qtfP, t hen 
 p IqgP and q ! p€P« 
 
 P< ; . Commutative law holds under alternation. If n,g£P 
 t hen p !q= | J p. 
 
27 
 
 P3. Associative law holds under alternation, i.e. if 
 p«q, r£P then 
 
 ( p ! c 1 ) .' r - p ! ( | ! r ) . 
 
 P4. There exists an identity element FAIL in P such that 
 nit- A I L=o. 
 
 P5. P is closed under concatenation. If o,q£P. th^n 
 p%q€:P and 
 q%p6'P. 
 
 P6. Associative law holds under concatenation 
 (n%q )%r=?o%(q%r) 
 
 P7. Distributive law holds 
 
 o % ( q 1 r ) = ( p r '/ 1 ) ! ( p%r ) a n d 
 (a!r)%p=(q%p) ! (r?«p) 
 
 Pci. There exists an inverse -n such that 
 nl-n-RIL 
 
 P9. p^rJULL =NULL/to-n 
 
PIO. Any oat torn formed by concatenations and 
 nit ernntions. 
 
 As n side remark, patterns, under the operations of 
 alternation md concatenation, form a rinu with unit 
 element i\i\iU6-\] as a result of PI through PIO. 
 
 3.2.1 De viation from. ^iiiliiULl 
 
 Pcaders familiar with SniJPUL4 'would nrobably notice 
 that P2, tiic commutativity of the alternation operations 
 (p!q=q!p) is not strictly valid in 3Mni3DL4;in addition, 
 pattern matching in SNUBUL4 returns only the first natch, 
 ratner than all the matches. 
 
 The non-commutati vity in SMG30L4 is actually imposed 
 by the Tact that 3IHDBUL4 systems are imolemented on serial 
 machines, "/here mat china is dnn<~> serially. In a serial 
 implementation, the users would arranqe the ilternntos in 
 the or tier of the likelihood of successfully match inn, to 
 
29 
 
 increase the probability of reducing the execution time. 
 With the u.se of parallel processors, the Lifting of thP 
 restriction on comnu tat ivi tv would be an advantage. A 
 special mode can be implemented to force the execution of 
 alternation in a sequential manner as defined in 5M0BUL4 
 if the order is imnortant. 
 
 i'lie fact that only the first match is souqht in 
 SNUBHL4 can also bo reqarded as a victim of the serial 
 implementation. Aqain, in our Proposed machine, the 
 programmer can decide whether he wants only t h r> first 
 match or all of the matches. Hardware is shown in the 
 next section which could detect the first match. 
 
 3.3 Ii.rn.c_ liojiiid. f-or P atte rn UaicMjoa AlgorLkim in MjJBDLA 
 
 Pattern matching in SNUB0L4 is done in almost an ad 
 hoc manner. The alnorithm for pattern matching used in 
 SNUB0L4, given in Section 2. 3.1, can easily be. imolemented 
 using stacks. Due to the unnecessary backtracking of the 
 alnorithm, the time required to metch two simnle strings 
 rnav bo as much as o ( pq ) , as in the case for [Hatching th^ 
 
3D 
 
 pattern A**pl3 and the subject strinq A.**qB (where o 
 indicates in the order of, and A**p denotes a strinn of o 
 characters of A). ;iith a sliohtly more complex oattern, 
 such as one with m alternates it would require as much as 
 mnq comparisons. '.Jhon concatenation is introduced, such 
 as 
 
 o=(/u :a; 5 : ... !Am) (Bi : n;>; ... !Bn) 
 
 assuming ! Ai 1 = 1 Bj • -!c, and the l^nnth of t ne subject strinq 
 
 is s, t no time increases to 2kmns. 
 
 As pattern matchinq is tno central feature and a very 
 time consuming process, it i'~ of paramount importance to 
 speed it id. 
 
 Faster serial oattern matchino algorithms for one 
 oattern and one subject strinn do exist [KNU74], requiring 
 orocessinq time o(m+n) for a subject strinn of lenqth n 
 
 and a oattern of length m. 
 
 An algorithm for pattern with alterna-tes also 
 exists[ AHUVii] , requiring processinq time proportional to 
 o(n+sum of the lenqtn of the alternates), where n is the 
 
31 
 
 lenath of tne subject strinn. Moth of t ho two faster 
 aloori t lirns require some preprocessing. The time for the 
 two faster algorithms quoted hern includes the tims needed 
 for the pre-processing. 
 
 The main weakness of these two algorithms ar n that 
 they hot i) require pre— processing, and storai^ for tables 
 generated during nre-orocessino is required. In the noxt 
 sections, we will present a schema which do«s not require 
 any pre-processing. 
 
 3.4 M_ii.Lt em liiitLcJaiiiQ. Met work 
 
 In general, a pattern P in SNUBDL can he expressed as 
 
 where each Ai j is a strinn, '!' denotes alternation, and 
 
 the space between ')' and '(' denotes concatenation. One 
 
 may view the statement as analonous to a product of r,\m. 
 If fully expanded, the above equation is 
 
 P^ Ai/ui-- dmlAz/lt, ■ A,j... I^^^..^ 
 
32 
 
 Uiven a subject string f such tint 
 f=t( I )t(2) ...t(s) 
 
 lot us define tlia oattern matching problem 
 
 I" \> 
 as a nroblem to find post-cursor positions for some c or 
 all c such that l^c^s. i-Je shall refer to a machine which 
 can perform this task as a pattern matching network (P.'-IM), 
 as shown in l-'iq. 3.4-1. A sub-mac hi n a of this network, 
 M(T f A)« v/hicn produces a bit string or vpctor of O's and 
 I 's 
 
 m(l ) . . .m(s-k+l ) 
 called the oost-cursoi — position-bit-vector for the inout 
 text t(l)...t(n) and one simple pattern a(l)...a(!c) as 
 input is called pattern matcher ( I'M ) , with the condition 
 tint m(i)=l whenever t ( i ) . . . t ( i+k-1 )=a ( I ) . . .a ( k) for some 
 i, l^i+k-l^n. 
 
33 
 
 To illustrate how the machine in Fig. 3. 4-1 works, let 
 us limit the pattern to the simplified case hplow, with 
 only a limited number concatenations: 
 
 /?= (A,\A,\...]/\ n ) fa I -a. I- IB*) f f 3.+. I 
 
 ■ = A8 l \A6*\...\MBn 
 
 By definition and using the nronerties of oatt^rns in 
 Section 3.2 
 
 V... 
 
 The last equation above suggests tnat the pattern 
 matching of a complex pattern ( Eq 3.4.1) can be broken up 
 (I) into simole pattern matching such as M(s,AI,c), and 
 M(s,f32,c), etc., where each A I , . . . , Am, B I , . . . , Bn represents 
 simple patterns, and (2) appropriate subtractions, and 
 union and intersection operations. Step I can be solved 
 by using PM where each PM takes a subject string and a 
 simple pattern as inputs, as shown in Stage I of 
 Fig. 3. 4-1. Since the output of the PM are bit vectors, 
 
34 
 
 1 subtraction, inters action nnd union may bo replaced by 
 shifting, ANOinq, and UlMno respectively as shown in 
 Staqes III throuqh STAGE IV of l-'iq.3.4-1. An example 
 connection for a particular pattern is nivon in Fin;. 3. 4-2. 
 
 Mote that in an of fori to save qates and storaqe, we 
 do not desiqn the PMN so that it works with the exnanded 
 forn 
 
 AIM1 ! ... ! \nf3n 
 as inputs, where wo use tho notation \i0.j to represent the 
 conca tona t ion of Ai and B.i. Tho output of Staae I are 
 strinas of bits, 3nd tho rost of tho staqes work with 
 those strinqs of bits instead of sbrinqs of character or 
 indices, resultinq in additional savinqs in qatos and 
 storaqe . 
 

 T- 
 
 aA 
 
 T 
 
 pm 
 
 X 
 
 T 
 
 B, 
 T. 
 
 Shift 
 
 J* 
 
 CZD-i 
 
 
 N 
 
 ;[/iw) s . 
 
 / 
 
 r 
 
 PaHtrn Broadcast Allan Vcclor 
 
 ^H 
 
 OR 
 
 ^ 
 
 3 
 
 Vfecrer 
 
 « 
 
 — r> %/ 
 
 Broadcast — broadcast each output vector M(T,Ai) to n 
 
 places, and each M(T,0i) to m Places. 
 
 Align— shift each M(T,Ai) that is to be AMDed with M(r,Bj) 
 
 in the next stag 9 inj!-! Ai! positions to tlr right if 
 
 ! B j .' > ! A i I ; else to the left. 
 
 Vector AND — vector AMU M(T,Ai) and M(T,f3j) for all i and 
 
 i. 
 
 Vector OR — UR the resultinn vectors of the previous staqe 
 to form ona vector. 
 
 Fig. 3.4-1 fhe different stages of PM! 
 
36 
 
 
 ?!Ai 
 
 ffl 
 
 Jt 
 
 <±J 
 
 \?M; 
 
 •\JY 
 
 477" I 
 
 \AW> 
 
 L S J 
 
 
 U 
 
 c/R p 
 
 WD 
 
 AVT^ 
 
 -T_P 
 
 o£ 
 
 "1 
 
 4a7> 
 
 H~ 
 
 S 
 
 c softer 
 
 ;. 3.4-3 Connoction for pattorn ( A I ! A: 5 . .' A3 ! A1 ) CHI i R2!n3! H4) 
 
3 7 
 
 3.4.1 ^t si CIO I 
 
 Three cii f f ercnt ways Lo implement Staoe I arc 
 considered: 
 
 1. Maximum Para 11 el (MP) 
 
 2. Pattern Serial (PS) 
 
 3. Serial usina Knuth, Morris , and Pratt's algorithm 
 (SKMP) 
 
 Method 1 (MP) 
 
 This method involves cornoarina the pattern in everv 
 possible oosition in relation to the subject strinq 
 simultaneously. fhis is the most parallel way 
 concei vable. 
 
 Conceptually, this met tod involves comparinq everv 
 character of the pattern with every character of the 
 subject strina and producinn a bit map as shown in 
 Fia.3.4.1-1. The next steo is to AND all these bits in 
 rjroups as outlined by the ellipses. 
 
Tho time bound for this is asymptotically aqual to locj2 s, 
 '.-/horn s is the l«mtn of L ho subjnct strini. 
 
39 
 
 Pi 
 
 P 
 
 ri 
 
 P3 
 
 
 i 
 
 iq. 3.4.1-1 Maximal parallel way of match inn 
 
 Method 2 (PS) 
 
 This in almost like Met no 
 
 except that only on 
 
 character of the pattern . is comoared with the whole 
 subject string at a time or snction of the subject strirvj 
 at a time. Mnr 5 may think of this as Method I compressed 
 
40 
 
 in space and expanded (iterated) in time in the 'pattern' 
 
 dimens ion. 
 
 The speed of thin method is very close to that of 
 
 Method I, especially for short mttern. Usim this 
 
 method, one may take advantarje of the fact that in tne 
 real world, the pattern is usually short. 
 
 Method 3 (SKMP) 
 
 I'his is an implementation of the method of 
 [ KMU74, AUG/ 3 J . The time required is n r on or t ion el to s 
 plus oreorocessing time. 
 
 3.4.1.1 C ompariso n qJL the Metho-Js 
 
 Amonq the three methods, 'IP represents the fastest 
 method with the highest in oate requirement. Hn the other 
 extreme, SKMP is the slowest and requiring the least 
 number of gates. Method 2, PfS, lies between MP and JKMP 
 in terms of nates and time. 
 
I'o further compare the merits of these throe methods, 
 we calculated the values of qate*time for all these three 
 methods. The results show that qate*time remains 
 approximately constant for all these methods? this, wo are 
 unable to select one of the above methods and incorporate 
 it into our design by basing our decision solely on the 
 qate*time criteria. 
 
 Eventually, PS, Met hod 2, was selected based on the 
 following reasons: (I) the performance is very close to 
 that of Motb.vl ] (.MP), especially for short patterns, 
 ( 2) preprocessing is not necessary, and (3) Method I is 
 very rigid: It can only process strings of a fixed length? 
 strings of length greater than it is designed for requires 
 additional messy work. Trie the other hand, Method 2 can 
 process strings of any length with equal ease, Method 2 
 can be regarded as the golden mean between the extremes. 
 The design is given in the following sections. 
 
 3.4.2 Holism, ox s_t.g.aa I 
 
 The function of the PM, l-'ig. 3. 4-2, is such that given 
 
42 
 
 the character strinq inputs p(l)...p(k) and t(l)...t(n), 
 t lie PH can nroduce b(l)...b(n). Tto bit vector 
 b(l)...b(n) is caller) tto nost cursor position bit vector, 
 whereby b(i) = l if p( I ) . . ,o(k )=t ( 1 ) . . . t ( i+k-l ) and 
 I < = i<i +k-l <=n. 
 
 1'ne machine which performs the function of PM of 
 Fiq. 3. 4-3 is shown in Pin. 3.4.2-1, and controlled by 
 Alqoritiim 3.4.2-1. The subject string is loaded into the 
 X registers X(l)...X(s), and one character of the oattprn 
 is nlaced in register P. 
 
 During each minor cycle, the character in P is 
 compared with each character in the X registers. The 
 result is ANDei with the content of I) and restored in D, 
 where each !) register to Ids a bit. The characters in the 
 X reoisters are shifted left and the next character of the 
 subject strinq is loaded into X(s). The next character in 
 the pattern is loaded into P register. The machine is now 
 ready for the next minor cycle. k of these minor cycles 
 constitute a major cycles, where !< is the lenith of the 
 pattern. 
 
4.3 
 
 After a major cycle, the content of D(l)...0(s) is 
 the post-cursor-position-bit-vector for the strinn in 
 X(l)...X(s) in til--- bo.qinnina of the major cycle. 
 
 Thm . If n>>s. then b(l)...b(n) can he obt 'lined in at 
 most n/s major cycles with t lie innuts l;(.l ) . .-. t (n) end 
 n ( I ) . . . p ( k ) . 
 
 Sketch of Proof. t ( I ) . . , t ( s ) . , .t ( s+k ) ar° taken in the 
 first major cycle to nroduce b(l)...b(s). t ( s ) . . . t( ?s+l: ) 
 are taken to nroduce b(s + 1 ) . . . b(2s ) at t ne saconH major 
 cycle, and so on. It is easy to convince oneself that it 
 most n/s major cycles are needed. 
 
 Clearly, to produce b( r ) . . .b( r+s-l ) , for some r such 
 thet l<r<s. the inouts t (r ).. .t( r+s-l )t(r+s )... t( r+s+k-2 ) 
 and p(J)...p(k) are needed. If t (r +s ) . .. t (r+s+k-2 ) do not 
 exist, i.e. the subject strina is too snort, it is 
 necessary to take NONE character (character which Hoes not 
 match any character) as t (r+s ) . . . t (r s-s+k-P. ). \s an 
 example, if the subject strinn is t ( I ) . . . t (m) , where 
 k^m<s, the initial loadinn of t's into X registers woui I 
 
44 
 
 leave X(n) empty for m<n£s. It is thus necessarv to load 
 X(n) for m<n ^s with NONE characters; furthermore, after 
 eacn minor cycle, a HUNE character has to he loaded into 
 X(s) also. 
 
4'5 
 
 P 
 
 x, 
 
 Jl 
 
 cn*ra.cter 
 c.o"<i«ra.tor 
 
 o 
 
 D, 
 
 X- 
 
 1 
 
 I 
 
 I 
 C~ch ar&cfe.r\ 
 
 
 [: 
 
 clqaraiter 
 
 C CT*£*tt&* 
 
 Fig. 3.4.2—1 A pattern mntcher 
 
4 6 
 
 Algorithm 3.4.2-1 
 
 load h's with 1 's (sot D's ) ; 
 
 r : = 1 
 
 load X(l)...X(s) with t(r) ...t(r+s-l). If not enounh 
 t's to fill nil t ho X registers, pad on tho rinht with 
 NO ML: characters i 
 ji = l ; 
 repeat 
 
 load P( i) ; 
 
 comoare, AM!) the result with the old !)(i); 
 .store new binary results into h(i); 
 shift content of X's left one character nosition; 
 if no more subject strinn await inn to 
 be processed, stuff a NONE character 
 into X ( s ) 
 else 
 
 X(s) receives the next character t; 
 j : •-- j + 1 ; 
 until j>lerv~jth of pattern; 
 rea lout D's. The bit vector former] by 
 tho content of L) ( 1 )...')( s) is a post -cursor- 
 position-bit-vector for t (r ) • .. t (r+s-l ) ; 
 set D's; 
 r: =r+s ? 
 until lennth of pattern>lenoth of remaininn subject string 
 t(r ).. . 
 
4 / 
 
 Tiie workinq of the PM can befit be illustrated by an 
 example. Let us use the subject strinn abcdefqh and the 
 pattern def. Fiq. 3.4.2-2a is a snaoshot of the content 
 of the registers before and after the first character 
 comparisons. After the first minor cycle, the contents of 
 X's are sliifted left one character position, the new 
 character e of the subject string is loaded into X(s), and 
 t,ie next character of the pattern, e, is also loaded into 
 re-lister V (Fig ,3.4,2-2b) . The routine of como.arison and 
 updating continues. 
 
 Fin. 3.4.2-2d marks the beginninq of the second 
 major cycle since the content of D represents t ne 
 post-cursor-position-bit-vector for t ne substring abcdef. 
 The bit vector in L), which is 0001, indicates that there 
 is a match at oosition 4 of the subject strinq. 
 
 In Fiq. 3. 4. 2 -2d, the contents of X registers are 
 shifted left k- 1 positions (wnere k is the lenqth of the 
 pattern), with successive character of t ne remaining 
 subject string enterirvn X(s) as it is vacated. Matching 
 begins for this new section 'of the subject strinq as it 
 
4 cj 
 
 did in l-i g. 3. 4. 2- 2 a . 
 
 riie s hi f t w hi c h takes place after I : in . 3 . 4 . 2 -2d 
 introduces a null character into X(s), as no more 
 characters are available from the subject strino. The 
 whole process terminates at Fici.3.4. 2-2f , when the lennth 
 of the strini in X registers is less than k. i'he comnlete 
 bit string obtained is 00010000. 
 
49 
 
 content of X (X( I ) . 
 
 content of P 
 
 content of D <L>( I ). 
 
 content of I) after 
 
 .X(s)) : 
 .D(s)) before 
 
 Kiq. 3.4. 2 -2 a 
 
 content 
 
 of 
 
 X 
 
 
 content 
 
 of 
 
 P 
 
 
 content 
 
 of 
 
 f) 
 
 before 
 
 content 
 
 of 
 
 D 
 
 after 
 
 content of X 
 
 content of P 
 
 contnnt of L) before 
 
 content of after 
 
 content 
 
 of 
 
 X 
 
 
 con ten t 
 
 of 
 
 P 
 
 
 content 
 
 of 
 
 u 
 
 before 
 
 con tent 
 
 of 
 
 D 
 
 after 
 
 Fin. 3.4.2-2b 
 
 Fig. 3. 4. 2-2 c 
 
 abed 
 d d d d 
 1111 
 1 
 
 b c d e 
 
 e e e e 
 
 1 
 
 1 
 
 c d e f 
 
 f f f f 
 
 1 
 
 1 
 
 e f a h 
 d d«d d 
 I I I 1 
 
 
 Fin. 3.4.2-2d 
 
 content of X 
 
 content of P 
 
 content of D before 
 
 content of after 
 
 content 
 
 of 
 
 X 
 
 
 content 
 
 of 
 
 P 
 
 
 content 
 
 of 
 
 [) 
 
 be fore 
 
 content 
 
 of 
 
 
 
 after 
 
 Fig. 3.4.2-2e 
 
 f n h A 
 
 e e e e 
 
 A =NDNE 
 
 q h A A 
 
 f f f f 
 
 
 
 
 
 Fiq. 3.4.2-2f 
 
130 
 
 3.4.2. I So god 
 
 Usina ocnott'cv TTL, Reich level of AN r )-oate de-lav is 
 roximately lOnsecs. Each minor cycle is thus about 10 
 nsocs. 
 
 3 . 4 . 3 j.La .io JUL 
 
 DRnotfi Lin outout of oach I'M of Staqe I by 'Uf,Ai), 
 whore i' is the text or subject strinq and Ai in the 
 pattern. 
 
 i'ho function of Staqe 1 1 is to broadcast the outout 
 vector or each '•', ( i" , a i ) to n olaces nnd the outout of each 
 
 M ( I", 1' i ) Lo in Dlaces . 
 
 3.4.4 S_Liiaa ILL 
 
 II is necessary Lo shift each vector 'UT,Ai) to he 
 ANDed with M(T,M.j) in StaqoIV !Mi!-!Ai! nlaces Lo the 
 riqnt (or Lo the left if ! 11.1 ! -! A I ! <0) Lo ensure that 
 vrc toi — AIJDinq in Staoe IV results in vector containing i 
 
51 
 
 bit ' I ' wherever Ai concatenated with Hi mate lies t he 
 subject strinn T. Denote the shifted result of this staqe 
 by S(.M(T,AI )) . 
 
 3.4.5 Stanp IX 
 
 Vector-AND 3(M(T,Ai)) with M(T,R.i) for all 
 
 combinations of i and j, where l^i^m, and l$'j^n. 
 
 3.4.6 S tage )L 
 
 Vector-fjr? the results of Stage IV, i'he m*n vectors 
 of staqe IV are reduced to one vector. The output is the 
 post— cursor — pos ition-bi t-vector of the pattern match of 
 the subject strinn T and pattern 
 
 (AI ! . .. ! Am) (Bl i ... Win). 
 
 3.4.7 afciiaa yjji 
 
 This stage converts the binary vector into a vector 
 of indices, using recurrences similar to the I's nosition 
 count, of Chen and Kuck [CIIE7 r J], 
 
52 
 
 3.4. U Likioa Vii2 
 
 ThI.s is the first-match r n coqnizer which consists 
 simnly of a tree of OR nates, which produces a 1 if any of 
 tie inputs is a 1 . If this output is I and the PMN is 
 operating at f irst-ma Lc n-onlv node, it Lnolies the 
 oresence o f n match in this major cvcle, _, nd Urn task of 
 the i ),: '.' is considered completer! wit I out further 
 process im. 
 
 ~> • '-> Gat e, l i ■ i ? , a nd ^ q L n '"'T ime 
 
 An estimate of the number of nates, the number of 
 gate-delays , and the product of the two are nivnn in 
 Ficf.3.LJ-1 through Fig. 3. 5-6 for Stage I of Method 1 and 
 Method 2, as a function of text length and oattern length, 
 ["he text lengtn denotes the length of the subject strinn 
 the processor can accomodate at one tine — it is Likened to 
 the word lenqth of an arithmetic orocessor. 
 
 i'i i. 'S.')-7 throti'ih l ; .i n.3.!5- If! sh'>w estimates of 
 total gates, lelay, and t i'ip nroduct of the two for rstaoes 
 
I tiiroucjh Stages VI of Method I and Method 2. The pattern 
 assumed is of the form 
 
 (Al ! ... !An) (HI ! ... !Bn> 
 
 and ! A I !-...! Bn !=k. 
 
5U 
 
 CTN 
 
 II 
 
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 0'9 
 
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 i 
 
 
 ITN 
 
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 to 
 
 
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 Pu 
 
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 o 
 
 -r cr: 
 
 I in 
 
 'J~> v 
 
 a 
 
 i — 
 
 D 
 
 CM 
 
 . 0) 
 
 X 
 
 i ° 
 
 ! r. 
 
 CV 1 
 
 o 
 
 H 
 I 
 
 CO 
 
 
 c ;: 
 
 ;.,_ 
 
 ■> • c; 
 
 2? 
 
 D'Gt 
 
 w; 
 
 V9c 
 
 il° 
 
65 
 
 ir\ 
 
 -r O 
 
 tOlX) 3WIlxJltfO 
 
66 
 
 4. MACHINE DESIGN 
 
 4 . 1 bvora 11 Ur o aniz. £ 
 
 Based on the characteristics of SNGBOL oroqrarns, we 
 have come up with the followinn list of items which a 
 machine should have in order to speed-up strinn 
 process inn . 
 
 I. Since memory reclamation is on° of the most 
 frequent activities, it is desirable that the rnemorv 
 unit has a memory reclamation orocessor (narbane 
 collector). This qarbaqe collector, synchronized 
 with the other memory accesses to wold races 
 [Jl'h/'jJ, would mark, relocate, update, and reclaim 
 unused memory spaces continually, independently of, 
 arid in parallel with other processors except for 
 synchron izat ion. 
 
 ?.. Pattern matching network which would sneed-up 
 most of the pattern matchinn orocesses, 
 
 3. Proqram instructions and data should ho kent 
 separate to abate access conflict, 
 
 4, Either a type conversion unit to convert between 
 
different types of data representation or an ALU 
 
 which performs Arithmetic in [3CD. 
 
 'j. Multi-function arithmetic logic unit. 
 
 6. Build into the memory units some facilities for 
 
 the transfer of data within tho memory, 
 
 I. Control unit which is capable of sync hron i /. inn 
 
 all t te parallel activities and avoid incorrect 
 
 sequencing. 
 
 d. II-' tree processor [DAY 72b] to evaluate doc is ion 
 
 trees. Results of program analysis snows that IF 
 
 trees of considerable lennth exists, that r nost of the 
 
 trees ^r a sparse, and that d ?/.'■' of the IF tr^es 
 
 analyzed are loss than six levels dean. A decision 
 
 processor of .six level capability would thus be 
 
 sufficient. Trees greater than six levels could be 
 
 solved by mapping into free nodes (folding) or 
 
 repeated use of the processor (iteration). 
 
 4 . 2 (jarbaae Collection 
 
 SflUBGL is a "typeless" language, meaninn that it is 
 declaration-free and that storage is not or fa 1 local'.od for 
 
OJ 
 
 variables, but rather, it is allocator! on riomand. When 
 storaqe is no lonqer needed, it is freed Butomatically bv 
 a process called qarbanc collection. or momorv 
 reclamation. Storaqe is no lonqer n^ede-i when, for 
 example, a variable is assinned a new strinq value; 
 consequently, the storaqe for the old strinn is no Lonoer 
 in use assuming taat it is not referred bo bv 'invt Iiin i 
 else. 
 
 Allocation of memory in :>NL)o'JL is very simnla. 
 Memory is Jivided into two regions* allocated and I'v^c. 
 reqions. dhen storane is o^ede I, il is taken fr">m the 
 boqinninq of the free reqion. 
 
 The basis qarbaqe collection alqorithn L -J!? 1 7T? ) works 
 as foil ows 3 
 
 1. Marl: — iden t if v storage area which is no lonqer neoda I 
 (or inaccessi ble) . 
 
 2. Relocate — compact the accessible cells into a 
 con c iquous reqi on . 
 
 3. Un late — pointer reference:; to relocated ca lis inva L i 
 be ni)fJa ted. 
 
69 
 
 Uarbaqe collection is a time consuminq orocess. 
 Fypically, a nroqram spends about 30-. of its execution 
 tine in garbaqe col lect ion [ (JIM /6 t STE / ! j] . TiTounh the use 
 of parallelism, we propose to overlao qarbaqe collection 
 with actual execution of the SHGBDL pronram. 
 
 i'lie garbaqe collector in our proposed machine is 
 essentially a processor whicn executes the three phases! 
 (1) mark, (2)relocate, and (3) update, in n irallel with 
 the other orocessors. The most important consideration of 
 this processor is its synchronization with other 
 orocessors, and a similar problem for tne case of 
 LI5PCMCC62J nas been discussed in some detail by 
 Steele[STE7!3] . 
 
 iJote that in addition to reclaiminq unused space, 
 continuous rjarbaoe collection has t Ian advantage of 
 
 imorovinq nrooram locality in a paqed memory system. 
 
 4.3 JLL free Processor 
 
 5NU13UL proorams tend to have a Larqe number of 
 
10 
 
 decision statements compared to numerical programs Like 
 l-"OftTf?AN. In order to speedup tiie execution of decision 
 statements, an IF tree processor [DAV72a] is used. The 1 1- : 
 
 troe processor receives the conditional result sot as 
 input, whereby each bit in the conditional result set 
 represents the result of a decision statement. fhe outnut 
 of the processor is the identification of the actual oatn 
 traversed due to the results of all these decision 
 statements. By executing all. t bo decision statements in 
 parallel, passing all theso results to the Ii- tree 
 processor and then choosing tho correct results dependi.nn 
 on the path, one is able to sneed-uo tiie execution of 
 decision statements which otherwise heve to bo processed 
 sequentially. The compiler algorithm for the IF Lrn^ 
 processor is sketched in Section 2.4.4. 
 
 A . 4 .Memory 
 
 iJefore discussing storage requirements end design, it 
 is necessary to consider briefly the internal data 
 representation of SMG13HL. 
 
/I 
 
 The basic unit of data ronrosontit i on in SMHRDL is a 
 descriptor, which i s n uniform representation of nil 
 IMUI. values md 1. ocn t ions . Fhe loscr.i a tor can ; >^ 
 t ho unlit of as the basic 'word' of the SK)! V "!1. system. 
 blvery value do serin tor contains a tyoe coin to indicate 
 the datatype and the associated \'-ilm. Values witn 
 limited field lennth, such as numbers, ire directly 
 represented in the descriptor. Values with unlimited 
 lencjtn, for example strinqs, are represented indirectlv by 
 a pointer to a memory location and perha >s an offset from 
 t na t locati )n. Consequently, menorv must he addressable 
 byte-wise an I Jescri ntor-wise , just is in ioi" computers. 
 locations c in ; ^e addressed both as a byte and as a wor I, 
 where a word is a multiple or bytes. Since the size of i 
 descriptor is far binder than a byte, a descriptor is tins 
 a mu.l t i pie of bytes . 
 
 Memory is divided into two distinct units! or on ram 
 memorv and data memory in order to en linn c= overlanoinn in 
 memory access. The oronrarn memory stores the sod") 
 aenerated bv como i 1 inn a SJ'l'df. source proqra . fiie I 
 memorv holds constants ml natural variables nenerated 
 
12 
 
 during the compilina and execution phases. 
 
 4.!3 Hr.cn ram Memory 
 
 The proaram memory consists of a hierarchy of stornqe 
 
 devices [ KUC'/O, MAT/2] — the cache memory, primary nroqram 
 
 rnemorv, and external storage such as CCD,maqnetic bubble 
 memory, disks, or drums. 
 
 4 . 6 Dat a Me m or y 
 
 The data memory is made uo of a number of memory 
 banks. As transfer within the memory (stemminn from 
 concatenation, qarbaqe collection, etc.) is important in 
 liNUBUL, soecial considerations are oiven to the design to 
 eedup / move / of a sequence of data, from one location to 
 a not her . 
 
 ["he general organization of a sinqle memory bank is 
 shown in I • in- I-.6-I. Tiie smallest addressable entity is .i 
 byte, and the largest addressable entity is a descriptor. 
 
73 
 
 to i 
 
 - 5 ! 
 
 ^ I 
 
 S : 
 
 ■"5 
 
 J 
 
 output register j 
 
 A^Jj 
 
 < 
 
 in. 4.6-1 A momory bank 
 
74 
 
 For a transfer within a bank, data ar^ read out to 
 the output register, gated into the innut register, and a 
 write cycle is initiated. Transfer between memory banks 
 may be performed via the fast inter-memory bun. The 
 inter -memory bus, Fio.4.6-2, is a simple barrel shifter 
 since transfer of a strirvi from one memory bank to anotiier 
 within i mult i -banks memory system can be regarded as 
 .shirts when looking at the memory ports, as si own in 
 Fiq.4. 6-3. 
 
/'J 
 
 (MtRZL SHIFTED 
 
 '4 J 
 
 w ouj 
 
 Afem, 
 
 //V 
 
 TZU« T 
 
 I I 
 
 Firj. 4. 6-2 Intor Mr 
 
 nory I jus 
 
16 
 
 A 8 C 
 
 
 
 A B C 
 
 
 P£ 
 
 
 
 before 
 
 - 
 
 
 
 
 
 transfer 
 
 ne./n l 
 
 Yltm^ 
 
 Mi 
 
 'M- 
 
 tiem. 
 
 £ 
 
 
 A 
 
 Bet) 
 
 
 
 A 
 
 
 
 z 
 
 
 , 
 
 i 
 
 
 after 
 transfer 
 
 tfem x MtiY). 
 
 l-'i'l. -1 . 6-3 i'iio effect of movina a strinci 
 
// 
 
 4. / Instr i. 
 
 jpt 
 
 Speed is by no means the only concern which remains 
 for string processing languages; imnlementation of such a 
 language, related software, and compilation of n roar ems 
 are also far more complicated on a conventional machine. 
 In ALu'UL, a statement of the form 
 A=B+C 
 
 can easily be compiled into 
 
 LUA:J B 
 ADD C 
 STURE A 
 
 whereas in SNOBOL, no similar sequence of codes can be 
 generated in the machine level for a string oneration .such 
 as pattern matching. The nap between the software and 
 hardware nas to be bridged by .sophisticated software. 
 With the proposer! machine organization, we can have an 
 instruction sat which includes the one mentioned below. 
 
hi 
 
 The instruction set of t no machine are oivon in Table 
 -!./-]. An address usually desinnates a processor roqister 
 or m a m o r y location. 
 
 In addition to the instructions frequently found in a 
 conventional machine, it has some instructions for oattern 
 constructions and pattern matchinq. 
 
/'? 
 
 APITIlh 
 
 L'1_L£ 
 
 ADD XI 
 
 »X2 
 
 SUB XI 
 
 ,X2 
 
 MPY X 1 
 
 ,X2 
 
 i) I V XI 
 
 ,X2 
 
 I NC X 1 
 
 
 DEC XI 
 
 
 UllG XI 
 
 
 NUM X 1 
 
 
 AND X 1 
 
 ,X2 
 
 nn x i , 
 
 X2 
 
 XUH XI 
 
 ,X2 
 
 nut xi 
 
 
 X2! 
 
 '=X2+X 1 
 
 
 X2i 
 
 =X2-XI 
 
 
 X2: 
 
 :=X2*XI 
 
 
 x;>! 
 
 i=X2/X 1 
 
 
 XI 1 
 
 :=X 1+1 
 
 
 XI i 
 
 i=XI-l 
 
 
 XI 
 
 !=-Xl 
 
 
 convor t X 1 to 
 
 a number 
 
 X2:=XI X2 
 
 
 X2:=XI X2 
 
 
 X2:=XI + X? 
 
 
 comol ement X 1 
 
 
 lbi oh cQiiniai 
 
 Guru x 
 uum x,c 
 
 unconditional branch 
 branch to x if the 
 condition specified 
 in C (EQ,Ni:,LT,LIi,GT,UfI) 
 matches the condition 
 specified in t ho 
 condition codo renister 
 
 U4IA liiAILiliUR 
 .WGV X I ,X2 
 
 transfer value in XI to 
 
 Y P 
 
 A <C 
 
 CUHPARISUN 
 CD.V.PM XI ,X2 
 
 CGMPS X1.X2 
 
 convert XI and X2 to 
 
 numbers 
 
 comoare them, and store 
 
 the result 
 
 of the comparison 
 
 (LT,EQ,GD 
 
 in the condition code 
 
 reqi st or 
 
 convert XI and X2 to 
 
 strinqs, comoare 
 
 them lexically, and set 
 
 the condition code 
 
 reaister . 
 
 Fable 4.7-1 Instruction sot (continued) 
 
60 
 
 TSTNULL XI 
 
 ALTERNATE X I ,/.' 
 
 CONCATENATE X I , X2 
 
 test if the value in XI 
 is null and 
 
 set the condition code to 
 EQ or ME 
 
 return in X2 the 
 alternation of XI and X2 
 return in X2 
 
 concatenation of XI to 
 X2 
 
 immediately assigns the 
 orotion nf the 
 subject strino matched by 
 
 CUNHI riGNAL -ASSIGNMENT XI , X2 
 
 cursor xi 
 
 P ATTERN MAIOILIG. 
 PATTERN -MATCH S,P 
 MATCH-AND-REPLACE S,P,f) 
 
 same as IMMEDIATE- 
 ASSIGNMENT excent that 
 t hp assignment occurs 
 on 1 v if t he na ttern 
 match is successful 
 assign cursor nosition 
 the location in XI 
 
 match S against P 
 match S aqainst P and 
 repine e the matched 
 substring in S by D. 
 
 f ] may be null. 
 
 to 
 
 Table 4.7-1 Instruction Set 
 

 L>. liMPiniCAL RESULTS 
 
 1 j. i Introduction 
 
 A sensible way to sneed-un or design a machine is to 
 study the characteristics of the program tnat cirn to l.v 
 run on that machine. To dcslnn a SHd^nL machine, it is 
 therefore desirable Lo study sons of the statistics of 
 typical SUOBUL programs, Gf course, there is no such 
 thins as tynical program or typical orogr anmer ; therefore, 
 we cannot trust any measurement to be verv accurate. 
 Nevertheless , it would give us an indication of what these 
 typical machine parameters arc. 
 
 static a n d Jynamic statistics are si van in this 
 section. Dynamic statistics are generally more useful for 
 computer Jesigners, althounh they are mor° lifficult to 
 net. Dynamic statistics usually include relative 
 frequency of usaoe of different oneratlons, and the amount 
 of Lime different operations take. -Jivn the relative 
 frequency >f u sarins of di fferent oper it ions i ; known, one 
 would know which operations the sneeduo attemot should be 
 
emphasized on. When the speed of different operations are 
 known, one will have a better idea on how to balance the 
 computer system. 
 
 b . 2 Static Freque ncy C ount 
 
 i ne results of the analyses of a sample of SilJCUL 
 programs are presented in this section. These proorams 
 were unprotected files stored on disks at the Computer 
 Services Uffice of the University of Illinois at 
 Urbana-Champaiqn. This sample of 4'j proorams, written bv 
 a wide variety of neoole, includes a ~iood cross section of 
 a noli cation pronrams; some ex amies' of which are those used 
 for text or file processing, job control lnnquaqe 
 processinq, artificial intelligence research, data entry, 
 
 languaqe preprocessor, etc. i'he total number of 
 statement.'] in the programs, and the proaram size 
 distributions are qiven in Fable L5.2-I and Table :5.2-2 
 respectively. From these distributions, one can perh i ■ 
 obtain an estimate of the si 7 e of oroqrarn memory n^ded. 
 
 ae static frequency count of different tyoes of 
 
i i 
 
 operators are summarized in Table 5.2-3. Une would 
 intuitively exoect this result tint arithmetic operators 
 would anpear less frequently than the strinn operators. 
 
 Frequency count of different keywords are shown in 
 Table 5.2-4. ANCHOR, which controls whether nattern 
 matchinci is to be oerformed in anchored mode is the most 
 frequently occurred keyword. 
 
 Accord inn to our analyses, 593 out of t he ?520 
 statements contain decision noto's. This result implies 
 that 23% of the statements are decision statement. I'he 
 occurrences of different type of 'goto' is illustrated in 
 fable 5.2-5. 
 
 I'he number of levels in each IF tree [hAV/Pb] is also 
 examined. Table 5.2-6 lists the result of the study. The 
 averaqe number of levels is approximately five, and the 
 median is four. fine further observation of the IF" trees 
 is that the IF" trees are generally very sparse. fhese 
 data pertaining to IF" trees would prove useful to the 
 desinn of IF orocessor. 
 
a a 
 
 Total number of executable statements 2520 
 
 Total number of comment statements 536 
 
 Total number of statements 3056 
 
 Total number of programs examined 45 
 
 Total number of labels 59 7 
 
 Total number of statements lonqer than BO c.nrs fti 
 
 Total number of statements with complex pattern 45 
 Table 5.2-1 Characteristic of program examined 
 
 lumber of statements (excluding noinmnnL) 
 
 itp' ii mnrv 
 
 I - 50 
 'j 1 - I : )0 
 101 -1 50 
 I 51 -200 
 201-250 
 2b 1-300 
 301 -350 
 
 32 
 6 
 3 
 2 
 
 1 
 
 
 Table 5.2-2 Proqrarn size 
 
yb 
 
 fyoe of oo era tors 
 
 concatenat i on 
 al torn at ion 
 pattern matching 
 assinninent ( = ) 
 
 arithmetic (+,-,*,LE, 
 
 / C / / / 
 
 . ) 
 
 percent of all operators 
 
 10.6 " a 
 
 3 . 9 % 
 10.0% 
 60. <J% 
 10.3% (99% involves + ,-) 
 
 4.2% 
 
 Table 5.2-3 Operators f requency 
 
 Keywords 
 
 ANCHOR 
 
 TH I M 
 
 DUMP 
 
 TRACE 
 
 FULL5CAN 
 
 Percent o f all '< e y word s 
 
 70% 
 
 2% 
 2% 
 
 2% 
 
 Table 1 j.2-4 Keywords count 
 
 Type of noto 
 : ( ) 
 :S( ) 
 
 :F( ) 
 
 Frequency count 
 
 2/4 
 305 
 332 
 
 fable 5.2-b Goto frequency 
 
■36 
 
 Heiqht (number of levels) 
 
 2 
 
 3 
 
 4 
 
 b 
 
 6 
 
 I 
 
 ii 
 
 9 
 
 10 
 
 I 1 
 
 12 
 
 13 
 
 14 
 
 lb 
 
 16 
 
 1 / 
 
 18 
 
 hreriuoncy 
 
 ?.b 
 
 15 
 
 12 
 
 / 
 3 
 I 
 
 
 3 
 
 
 22 
 
 34 
 
 Table 5.2-6 Heiqht of IF trees 
 
 Lennth of string constant 
 
 I- b 
 
 6-10 
 I 1 - I b 
 1 6-20 
 21-2! 
 26- 
 
 Percent 
 69% 
 I 3% 
 
 4% 
 
 3% 
 
 2% 
 
 9% 
 
 Table 5.2-7 
 
-w 
 
 5 . 3 Dynamic S tatistics 
 
 ii)'? dynamic statistics r°forr n d to in this thesis arc 
 those of Uimpel [GIM76J. These results are summarized 
 here in Table 5.3-1. Tne oriqinal measurement [UIM76] was 
 cione on SITB.HL, which is an interpreter, fhe values in 
 Table 5.3-1 has been obtained from [GI'VT/6] after 
 renorma 1 i 7i rio to mask off the effect of the interpreter, 
 and qrouned into the five categories shown in fable 5.3-1. 
 
 Tyoe of operation oar cant of total 
 
 time scent in program 
 
 garbage 'collection 31.5% 
 
 strinn processing 25.2 f> 
 
 pattern matching 16.1% 
 
 I/O 11.23 
 
 others 16.0% 
 
 1'abla 5.3-1 Execution time distribution 
 
88 
 
 6. SYSTEM PARAMETERS 
 
 6 . i ImroducU m 
 
 rue following sections will describe the system 
 parameters of the machine described in Chanter A . 
 
 6.2 Usscxi o tor LLLzji 
 
 scriotor, as implemented in SMU13UL on the H3M 360, 
 occupies n double word (6-1 bits). The CUC 6000 descriotor 
 is ono word (60 bits). .in choose n descriptor size of 64 
 bits since it seems to be t tie smallest descritor .si 7.0 that 
 is a nower of two and also adequate for its nurnose, as 
 manifested by the implementations of SN0I30L for IBM 360 
 n I CUC 6 . 
 
 6 . 3 U escri otor i-ormat 
 
 All f.i ita objects in SiKJfHJL ere representee 
 descriptor. Descriotor in our machine iwve t ne forn 
 
 )V 
 
 V 
 
d9 
 
 l'ne F field is a flag which identify the type of the 
 descriptor The l ; field contains 3 bits. 
 
 Tne T field represents the size of the object in the 
 V field or nointed to by the V field. Twentv-f our bits 
 are allocated to the T field, allowing it to indicate 
 
 1 en nth of string of up to 2** 2 A bytes lonn. The 3? bits 
 allocated to the V field allows it to represent inteoern 
 in the ranne -2**31 to (2**31)-!. r ?eal numbers may have 
 the approximate ranne of IO**-78 to 10**73. Pointers 
 (address), when "s^d in this field, may nave the ranne of 
 to (2**23)- I . 
 
 6.4 ciAjaEa.c.t er Sizs. 
 
 We oronose that our machine use 3-bit characters 
 since it is conveniently a power of two and it provides a 
 laroe enough character set that is useful in text 
 processing. An 8-bit character will also orovide a 
 character sot which includes a special character which 
 matches any character and a character which does not match 
 any character. 
 
I 
 
 6 . j ALU Pr oce s sor 
 
 . ie \LU processor is a multifunction orocessor with 
 one unit for division, ono for multiplication, and .six 
 units of adder since 99-'o of the arithmetic (such as 
 
 Idition, subtraction, test for nrenter then, equality, 
 
 ;c . ) r ■ j'.ii re the adder. 
 
 >n j the proqrams analyzed, there ere only five 
 statements which require multiplication or division; thus, 
 >\ each is used in our machine. Six adders are 
 chos t no sake of convenience (so that the total 
 number of functional units add no to einht), A :nnr^ 
 accurate reflection of the number of adders needed can be 
 ibtaii I ■ transforminn the ororjrams and countinq the 
 number a ffitions rend subtractions that can be carried 
 oat, i n far illel , 
 
 r a 1 loqi c .processors (AND an I '];) ir n used in tfv 
 ttern hi no no twork . 
 
6.6 LL 'lx_££ P_r.Q,ccs_£Qr 
 
 Statistics from proqram anslysis indicates that 
 anoroximately 25 o of the statements in a nrooram are 
 decision statements, which aqrees verv well with the other 
 lahqunqes, such as CUDULC5TR74] and (JP55L UAV74b] . file 
 average number of levels for the decision tr°e is five, 
 and tuat the tree is very sparse; thus, a decision 
 processor that can lendle a six levpl decision tree should 
 he su ff ic i ent . 
 
 .;ith a six level decision orocessor,it can handle at 
 least six decision statements at oncn. In view of this 
 qrouoinn of six decision statements into one, the 
 percentage of decision statements in a program may be 
 reqarded as 4''-'. Consequently, ono IF tree processor for 
 our machine is sufficient. 
 
 6 . 7 P rogram Memory 
 
 As can be seen in Table b.2-2, SMUI3QL oroqrams are 
 generally small in size. To obtain an estimate of the 
 
9 I 
 
 number of words npoded for the nroorarn mnmorv, wo assume 
 (I) most programs are loss than 3'30 statements lona, (2) n 
 safe estimate of 10 words (64 bits) of machine 
 instructions are needed for each statement. Usinn the 
 above assumption, a pronram memory of 41< words will be 
 i -lequato. 
 
 ■ . > LLiLa P rio r y 
 
 i'ho number of data memory banks required is 
 determined by the memory bandwidtn required. Fho PM.'l 
 requires 9 new characters from the memory nor minor cycle 
 (VOnsecs), one character for the text and eiqht for tiie 
 patterns? consequently, the necessary bandwidth is 9 
 characters nor /() nsecs. 
 
 Fiuming one microsecond memory is used, a simple 
 calculation shows that sixteen banks of memory, each with 
 a descriptor size of 6A bits (y characters) are needed to 
 fulfill the memory bandwidth requirement. 
 
9 \ 
 
 6. 10 PMN 
 
 Based on the observation of pattern matchinn in 
 SNQBGL, we propose a PMN that can take patterns of the 
 form 
 
 pattern = ( Al I A2 .' A3 .' A4) ( B1 ! R2 ! H3 ! B4 ) 
 
 where Ai and Bj are strings. The connection can be 
 changed to handle patterns in other torn. A P.MN of thus 
 complexity contains eight pattern matchers, and can also 
 he use') ^r^ eight pattern matchers by intercept ino the 
 output of S tage I . 
 
 The PMN also contains 64 AND-orocessors , each of 
 which can AMI) two 64 bit vectors, producing a 64 bit 
 vector as a result. In addition, the PMN also has 32 
 GR-orocessors . 
 
 The parameter s (section 3.4., ; ) of the pattern 
 matcher is chosen to bo 128. 
 
94 
 6.11 L-'xnected S peedup 
 
 Uith the autonomous qarbaqe collector, qarbaqe 
 collection time is expected to aonroach zero. 
 Concatenation, in SPITBOL, requires 0.05+0. 000'3n 
 milliseconds on an IBM 360, where n is the number of 
 r: ivir-ir. tors involved. In our system, only one microsecond 
 is needed to nov? I2i3 bytes? thus, the concatenation time 
 of our system is anproximately n/\?.3 microseconds. fne 
 speedup (time for SPlTDUL/time for our system) is about 
 640 for larqe n. 
 
 Pattern matchinq time is t lie sum of toe time for 
 subject evaluation, pattern buildinq, scanninq, ind object 
 evaluation nrvJ replacement. i'he replacement operation is 
 aooroximately equivalent in time to two concatenations, 
 and we have already seen the speedup achievable. 
 
 In SPITBUL, nattern matchinq for 
 
 p ^ nupu 'A', ioo) 
 
 *> ( 'A' 'B') 'C 
 
9 1 j 
 
 requires 12 milliseconds plus overhead. Usinn our 
 machine, the time is approximately 30 nanoseconds (?0 rjate 
 delays * IU nanoseconds per qate). The speedup in this 
 case is I .2*1 0**6. 
 
96 
 
 /. CDNCLUSIOiI 
 
 i'Jfi have pointed out some arcnitocturnl raqui .rements 
 for a lanrjuaqe like 5NGBGL, proposed an organization for 
 thfi machine, and sunqestad <->omn transformations and 
 compiler aloorithrns tnat can be use I on SflGiiriL. '/Je hnva 
 also estimated the amount of spea inn achievable usinn the 
 special hardware mentioned oar I i or'. 
 
 i - .' araa^ are onenad nn for mora research hv this 
 project. I : irst of all, mora dynamic statistics on 3 : IUHnL 
 are desirable. Secondly, some simulations can bo done to 
 determine more accurately the spaaduo achievable. 
 
 Si. nul -i L ]' on and pronram analysis for R.JUflJAM has baan noinn 
 on for- quit a 'i few years tlUJC/.'J. 
 
97 
 
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 [AIKJ/'jJ Aho,A.V. and Corasick, M.J. "Efficient Strinrj 
 Matching! An Aid to Bibliographic Search," Comm.ACM, 
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 [DAC59] Backus, J. J. The Syntax and Semantics of t no 
 proposed International Algebraic Lannunnr 3 of the 
 Zurich ACM-GAMM Cnnforoncn," Proc. International 
 Conf. on Information Processing. UNESCH (1959). 
 125-1 32. 
 
 tC!ll.:/'j.l Chen f S.C. and Kuck,D.J. "Combinational Circuit 
 Synthesis with Time and Cornnon^nt Hounds," Dept. of 
 Cornp. Sci. Rep. No. 713-7/5, Univ of Illinois, 
 Urbane . 
 
 [CUH65] Cohen f !<. and Uegstein, J.H. "AXLE! An Axiomatic 
 Language for Strinn Transformations," CACM il, I I . 
 
 [UAL)6u>J Dadda,L. "Some Schemes for Parallel Mult ioli ers, " 
 LLtn £E£OUen,za, 19., 5, 349-3 56. 
 
 [DAV72a] Davis, E. /I. "Concurrent Processinn of Conditional 
 Jump Trees," C UM PC 111 ±z LiLansi af_ ea.aexji, 2/9-2SI. 
 
 [DAV72bJ Davis, E.l'i. "A Mul t iorocessor for Simulation 
 Aonl i cat ions , " Ph.U Thesis, Univ. of Illinois et 
 
yd 
 
 rbana-C h'-iinpaion , Pept. of Gomp. Sci. Pen. Ho. 
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BLIOGRAPHIC DATA 
 EET 
 
 1. Repott No. 
 
 UIUCDCS-R-77-907 
 
 "Title and Subt itlc 
 
 Multiprocessor for String Manipulation 
 
 3. Recipient's Accession No. 
 
 5. Report Date 
 
 October, 1977 
 
 6. 
 
 Author(s) 
 
 Wing Kai Cheng 
 
 8* Performing Organization Rept. 
 
 No -UIUCDCS-R-77-907 
 
 ' Performing Organization Name and Address 
 
 University of Illinois at Urbana-Champaign 
 Department of Computer Science 
 Urbana, Illinois 61801 
 
 10. Project/Task/Work Unit No. 
 
 11. Contract /Grant No. 
 
 US NSF MCS73-07980 
 
 Sponsoring Organization Name and Address 
 
 National Science Foundation 
 Washington, D. C. 
 
 13. Type of Report & Period 
 Covered 
 
 Master's Thesis 
 
 14. 
 
 . Supplementary Notes 
 
 Abstracts 
 
 A machine organization is proposed for the fast processing of SN0B0L programs. 
 Measurements of SN0B0L programs are given to support various choices. Since 
 pattern matching is a major time consumer in SN0B0L, special hardware is proposed 
 for it. Several alternative designs were studied in detail and cost-effectiveness 
 measures are given for these. 
 
 Key Words and Document Analysis. 17a. Descriptors 
 
 High-level language architecture 
 Pattern matching processor 
 SN0B0L machine 
 SN0B0L measurements 
 
 b. Identifiers/Open-Ended Terms 
 
 c. COSATI Field/Group 
 
 .Availability Statement 
 
 Release Unlimited 
 
 RM NTIS-38 ( 10-70) 
 
 19. Security Class (This 
 Report) 
 
 m 
 
 UNCLASSIFIED 
 curitv Class (Thi 
 
 20. Security Class (This 
 Page 
 
 UNCLASSIFIED 
 
 21. No. of Pages 
 
 106 
 
 22. Price 
 
 USCOMM-DC 40329-P7 1