Avoiding Latch Formation in Regular Expression Recognizers

Specialized silicon compilers , or mod川e generators. are promising tools for automating 出巳 design of custom VLSI chips. In p缸ticular, generators for regular language recognizers seem to have many applications.ηus paper identifies a problem ca11ed latch fo口nation 出at causes 陀gular e x. pression recognizers to be more ∞mplex 由矶山ey would first ap阿ar. If recognizers are constructed in the most straightforward way 行。m certain regular exp陀ssions. 由ey may contain extraneous latches 由at cause incorrect operatio皿 After identi句ing 由e problem. 由e paper presents a "source-to-source" transformation 由at converts 陀但lar e x. pressions 由at cause latch fonnation into expressions 由at do no t. This transformation a110ws regular expression recognizers to be simpler and smaller,由us adding to 由e advantages of speci a1 ized silicon compilers. 1. lntroduction One of the most important tools available to today' s designers for speeding up 由epro臼ss of designing custom VLSI is the specialized silicon compiler. Sometimes ca1 led module generators. specialized silicon compilers are t∞Is 由at combine knowledge of a specific application area with a set of primitive cells and rules for combining rhe cells to produce a layout. Speci a1ized silicon compi1ers will only produce layours for rheir speci a1 ized areas of application. but will do a ve叩 good job within those areas. The chips 出at 由ey produce will be sma11 and fas t. Speci a1ized silicon compilers have been bui1t for digita1 signal processors 币, 14] , combinaúonal logic [16 ], data parhs [3 , 11 , 13] , general-purpose processors [17] , synchronizers [2,坷, and 由e topic of 由is paper, pattern matchers 凹, 12]. Anyrhing 出at improves 由e efficiency of rhe chips produ臼d by specia1 ized silicon compilers is a worthwhile contribution ω 由e field of VLSI design automation. This paper discusses specialized s i1icon ∞mpilers 由at produce recognizers for 陀引1ar expressions. A regular expression recognizer is a pattem matching circuit in which rhe pattern is specified by a 陀gu1ar expression. A specia1 ized si1 icon compiler for these recognizers will ac臼pt a regu1ar expression as input. and produce the layout of a recognizer for 由at expression.. Regular exp陀ssions have seen wide app1ication in computer science; among other tasks. 由ey have been used to specify lexica1 analyzers for programming languages , conrro l1ers for sequentia1 machines. filters for on-thet1y database search, pattems in image procεssing , and communication protocols. Regular expression recognizer百出erefo陀 have wide application, and are an especially promising application area for specialized silicon compi1ers. The contribution of this paper is a "source-to-source" transformation of regular expressions 由at allows more efficient recognizers to be constructed for them. The most straightforward circuirs for constructing regular expression recognizers exhlbit a problem: 陀cognizers for some expressions contain superfluous latches due to interactions between the ce l1s. Formation of rhese latches leads to recognizers 由at function incorrectly. Previous solutions to 由e problem of latch formation have used more complicated circuirs to elirninate or 陀set 由e latches. 节1ese more comp1icated circuirs increase rhe size of recognizers. and may make them run more slowly. The transformation introduced in this paper eliminates the expressions that cause latch formation , and so allows rhe simple , straightforward circuits to be used for a11 expressions.ηlÎ s a110ws specialized silicon compilers to produce efficient 陀∞gnizers for r吨ular languages. 2. Regular Expression Recognizers This section gives a notaúon for regular expressions and describes how to compile rhem into circuits. Straightforward ∞mpilation of some reμar expressions leads to a problem called lalch formation , in which extraneous latches 缸穹 formed within the compiled circuit These latches lead to incorrect operation.η1is section indicates how the problem anses and mentions some techniques 由at have been used to combat it A r它gular expression descnbes a reguJar language over some a1 phabet L. A regular exp陀ssion may 陀P陀sent 由e empty set (臼),由e empty s tIÍ ng (E) , or any set of s町ings 由at can be built up by concatenation , union and repetition from E and the single characters of L. A regular expression over L may include some characters 由at are not in L , such as operators and paren由eses. Assuming 由at 由巳