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Automata implementation : 4th International Workshop on Implementing Automata, WIA'99, Potsdam, Germany, July 17-19, 1999 : revised papers PDF

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Lecture Notes in Computer Science 2214 EditedbyG.Goos,J.Hartmanis,andJ.vanLeeuwen 3 Berlin Heidelberg NewYork Barcelona HongKong London Milan Paris Tokyo Oliver Boldt Helmut Ju¨rgensen (Eds.) Automata Implementation 4th International Workshop on Implementing Automata, WIA’99 Potsdam, Germany, July 17-19, 1999 Revised Papers 1 3 SeriesEditors GerhardGoos,KarlsruheUniversity,Germany JurisHartmanis,CornellUniversity,NY,USA JanvanLeeuwen,UtrechtUniversity,TheNetherlands VolumeEditors OliverBoldt Universita¨tPotsdam,Institutfu¨rInformatik August-Bebel-Straße89,14482Potsdam,Germany E-mail:[email protected] HelmutJu¨rgensen Universita¨tPotsdam,Institutfu¨rInformatik and TheUniversityofWesternOntario,DepartmentofComputerScience London,Ontario,CanadaN6A5B7 E-mail:[email protected] Cataloging-in-PublicationDataappliedfor DieDeutscheBibliothek-CIP-Einheitsaufnahme Automataimplementation:revisedpapers/4thInternationalWorkshopon ImplementingAutomata,WIA’99,Potsdam,Germany,July17-19,1999. OliverBoldt;HelmutJürgensen(ed.).-Berlin;Heidelberg;NewYork; Barcelona;HongKong;London;Milan;Paris;Tokyo:Springer,2001 (Lecturenotesincomputerscience;Vol.2214) ISBN3-540-42812-7 CRSubjectClassification(1998):F.1.1,F.4.3,I.2.7,I.2.3,I.5,B.7.1 ISSN0302-9743 ISBN3-540-42812-7Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violationsare liableforprosecutionundertheGermanCopyrightLaw. Springer-VerlagBerlinHeidelbergNewYork amemberofBertelsmannSpringerScience+BusinessMediaGmbH http://www.springer.de ©Springer-VerlagBerlinHeidelberg2001 PrintedinGermany Typesetting:Camera-readybyauthor,dataconversionbyPTP-Berlin,StefanSossna Printedonacid-freepaper SPIN:10840850 06/3142 543210 Foreword This volume contains the revised versions of papers presented at the fourth international Workshop on Implementing Automata (WIA), held 17–19 July, 1999, at Potsdam University, Germany. Asforitspredecessors,thethemeofWIA99wastheimplementationofauto- mataandgrammarsofalltypesandtheirapplicationinotherfields.Thepapers contributed to this volume address, among others, algorithmic issues regarding automata,imageanddictionarystoragebyautomata,andnaturallanguagepro- cessing. In addition to the papers presented in these proceedings, the workshop in- cluded a paper on quantum computing by C. Calude, E. Calude, and K. Svozil (published elsewhere), an invited lecture by W. Thomas on Algorithmic Pro- blems in the Theory of ω-Automata, a tutorial by M. Silberztein on the INTEX linguistic development environment, and several demonstrations of systems. The local arrangements for WIA99 were conducted by Helmut Ju¨rgensen, Suna Aydin, Oliver Boldt, Carsten Haustein, Beatrice Mix, and Lynda Rob- bins. The meeting was held in the Communs building, now the main university building, of the New Palace in the park of Sanssouci, Potsdam. The program committee for WIA99 was: A. Bru¨ggemann-Klein Technische Universit¨at Mu¨nchen J.-M. Champarnaud Universit´e de Rouen F. Gu¨nthner Universita¨t Mu¨nchen H. Ju¨rgensen Universita¨t Potsdam and University of Western Ontario D. Maurel Universit´e de Tours D. Raymond Gateway Group Inc. K. Salomaa University of Western Ontario W. Thomas Rheinisch-Westf¨alische Technische Hochschule Aachen B. Watson Ribbit Software Systems Inc. D. Wood Hong Kong University of Science and Technology S. Yu University of Western Ontario The work of the program committee, the reviewers, and the local arrange- ments team is gratefully acknowledged. AtthegeneralWIAmeetingitwasdecidedtorenameWIAintoInternational Conference on the Implementation and Application of Automata (CIAA)andto hold the first CIAA, that is, the fifth WIA, in London, Ontario, Canada, in the summer of 2000 in conjunction with the Workshop on Descriptional Complexity of Automata, Grammars, and Related Structures (DCAGRS) and a special day devotedtothe50thanniversaryofautomatontheory.Thecompleteeventwould be called Half a Century of Automaton Theory. March 2001 H. Ju¨rgensen Table of Contents FA Minimisation Heuristics for a Class of Finite Languages ............. 1 J´eroˆme Amilhastre, Philippe Janssen, Marie-Catherine Vilarem SEA: A Symbolic Environment for Automata Theory................... 13 Philippe Andary, Pascal Caron, Jean-Marc Champarnaud, G´erard Duchamp, Marianne Flouret, E´ric Laugerotte Analysis of Reactive Systems with n Timers .......................... 27 Anne Bergeron, Riccardo Catalano Animation of the Generation and Computation of Finite Automata for Learning Software.................................................. 39 Beatrix Braune, Stephan Diehl, Andreas Kerren, Reinhard Wilhelm Metric Lexical Analysis ............................................ 48 Cristian S. Calude, Kai Salomaa, Sheng Yu State Complexity of Basic Operations on Finite Languages.............. 60 C. Caˆmpeanu, K. Culik, K. Salomaa, S. Yu Treatment of Unknown Words ....................................... 71 Jan Daciuk Computing Entropy Maps of Finite-Automaton-Encoded Binary Images .. 81 Mark G. Eramian Thompson Digraphs: A Characterization.............................. 91 Dora Giammarresi, Jean-Luc Ponty, Derick Wood Finite Automata Encoding Geometric Figures ......................... 101 Helmut Ju¨rgensen, Ludwig Staiger Compressed Storage of Sparse Finite-State Transducers ................. 109 George Anton Kiraz An Extendible Regular Expression Compiler for Finite-State Approaches in Natural Language Processing...................................... 122 Gertjan van Noord, Dale Gerdemann Multiset Processing by Means of Systems of Finite State Transducers..... 140 Gheorghe Pa˘un, Gabriel Thierrin A Structural Method for Output Compaction of Sequential Automata Implemented as Circuits ......................... 158 M. Seuring, M. Go¨ssel VIII Table of Contents An Algorithm to Verify Local Threshold Testability of Deterministic Finite Automata .................................... 164 A.N. Trahtman A Taxonomy of Algorithms for Constructing Minimal Acyclic Deterministic Finite Automata ....................... 174 Bruce W. Watson Author Index.................................................... 183 FA Minimisation Heuristics for a Class of Finite Languages J´erˆome Amilhastre, Philippe Janssen, and Marie-Catherine Vilarem Laboratoire d’Informatique de Robotique et de Micro´electronique de Montpellier (UMR CNRS-Univ Montpellier II), IFA, 161 rue Ada 34392 Montpellier cedex 5, France {amilhast,pja,mcvil}@lirmm.fr Abstract. In this paper, we deal with minimization of finite automata associatedwithfinitelanguagesallthewordshavethesamelength.This problemarisesinthecontextofConstraintSatisfactionProblems,widely usedinAI.Wefirstgivesomecomplexityresultswhicharebasedonthe strong relationship with covering problems of bipartite graphs. We then use these coverings as a basic tool for the definition of minimization heuristics, and describe some experimental results. 1 Motivations ManyAIproblemscanbeexpressedasConstraintSatisfactionProblemsorCSP for short [Mon74]. A CSP involves a finite set of variables, a finite set of values forthevariablesandasetofconstraints.Eachconstraintisdefinedasarelation on some subset of variables and gives the values which are mutually compatible for these variables. A solution is a value assignment to variables that satisfy all the constraints. Most of the CSP’s works deal with the problem of computing onesolution.Nevertheless,insomeapplications(e.g.designproblems),itisnec- essary to compute and represent all the solutions. In this paper we address the issue of representing and computing all solutions. One approach for this problem, proposed by Vempaty [Vem92], is to use Finite Automata (FA)1. Given a permutation of the variables set, the set of solutions appearsasaregularlanguageandcanberepresentedbyitsMinimalDeterminis- tic Finite Automata (MDFA). Solution sets languages (Ln) are finite sets words of equal length. Using FA allows incremental construction of the solutions set by applying classical operations on FA associated to each constraint. The effi- ciency of this method depends on the size of intermediate MDFA. Computation of MDFA recognizing finite languages has been studied in [Rev91,DWW98]. In thispaper,weproposeamorecompactrepresentation:NonDeterministicFinite Automata(NFA).ItiswellknownthatNFAmaybeexponentiallymorecompact than equivalent DFA ; this property is preserved on the Ln class. However NFA minimization is an harder problem. The only studies on this problem concern the general case [Kim74,MP95,KW70] . In this paper we study this problem on the language class Ln. 1 AsimilarapproachusingOBDDshasbeenusedinordertorepresentbooleanfunc- tions [Bry86]. O.BoldtandH.Ju¨rgensen(Eds.):WIA’99,LNCS2214,pp.1–12,2001. (cid:1)c Springer-VerlagBerlinHeidelberg2001 2 J. Amilhastre, P. Janssen, and M.-C. Vilarem 2 Definitions In the rest of this paper, we focus on FA recognizing Ln languages. We will use the following notations. A finite state automaton A is a quintuple (Q,Σ,δ,I,F) where Q is a set of states, δ is the transition function Q×Σ → 2Q, I and F are respectively the start and the accepting states. We consider only automata with an unique final state since such automata are sufficient to recognize Ln languages. Therightlanguage (resp.leftlanguage)ofastateqisL (A,q)={m∈Σ∗ /F ∈ D δ∗(q,m)} (resp. L (A,q) = {m ∈ Σ∗ / q ∈ δ∗(I,m)}). In what follows, we will G supposethatallstatesareaccessible(theirleftlanguageisnotempty)andcoac- cessible(theirrightlanguageisnotempty).Todenotethetransitionfunction,we will also use γ+(q)={(d,q(cid:6)) / q(cid:6) ∈δ(q,d)} and γ−(q)={(q(cid:6),d) / q ∈δ(q(cid:6),d)}. A A AutomatarecognizingLnlanguageshavespecialproperties.First,sinceLnlan- guages are finite, they are acyclic. Moreover, since all words are of equal length, set Q can be decomposed into levels. For a given state q, all the words of its left language have the same length i. We will say that i is the level of q and denote by N (i) the set of states on level i. An automaton recognizing a Ln language A L⊆Σn has n+1 levels and is such that N (0) ={I} and N (n) ={F}. A A This work deals with the minimization of nondeterministic FA (NFA) and unambiguous FA (UFA). A UFA is an NFA in which there is a unique accept- ing computation for every accepted strings. The Flower Automaton is a distin- guished automaton among all UFA recognizing the same Ln language. Definition 1. Let L ⊆ Σn, the Flower Automaton of L is a UFA A = (Q,Σ,δ,I,F) such that ∀q ∈Q\{I,F} |γ+(q)|=|γ−(q)|=1. It is the biggest A A UFA recognizing L. The use of NFA is motivated by the fact that NFA can be more compact than the equivalent MDFA. For general languages, the MDFA equivalent to a k-state NFAmayhave2k states.Thefollowingexampleshowsthatsuchasizedifference also exists between UFA and MDFA recognizing Ln languages. (cid:1) Let Σ ={1,2,...,n} and L = (Σ−j)n−1.j ⊂Σn. n j∈Σ Consider the FA A with the following n+1 levels : n N (0)={q } N (n)={q } N (i)={q ,q ,...,q } (0<i<n). A 0,1 A n,1 A i,1 i,2 i,n The A transition function is defined by : n ∀i∈{1,2,...,n−2}, ∀p∈{1,2,...,n}, ∀j ∈Σ−p, δ(q ,p)=q δ(q ,j)=q δ(q ,p)=q . 0,1 1,p i,p i+1,p n−1,p n,1 Figure 1 shows A and its equivalent MDFA. A is an UFA recognizing L . 3 n n It has n×(n−1)+2 states. For the equivalent MDFA, the number of states is greater than 2n since for each non empty proper subset ofΣ there exists a state of N (n−1). A 3 Complexity of FA Minimization for Ln Languages For general languages, FA minimization is PSPACE-hard [JR93]. In order to studythecomplexityofFAminimizationforLnlanguages,weintroducerelated problems on bipartite graphs.

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