Algebraic Informatics: 4th International Conference, CAI 2011, Linz, Austria, June 21-24, 2011. Proceedings PDF
Preview Algebraic Informatics: 4th International Conference, CAI 2011, Linz, Austria, June 21-24, 2011. Proceedings
Lecture Notes in Computer Science 6742 CommencedPublicationin1973 FoundingandFormerSeriesEditors: GerhardGoos,JurisHartmanis,andJanvanLeeuwen EditorialBoard DavidHutchison LancasterUniversity,UK TakeoKanade CarnegieMellonUniversity,Pittsburgh,PA,USA JosefKittler UniversityofSurrey,Guildford,UK JonM.Kleinberg CornellUniversity,Ithaca,NY,USA AlfredKobsa UniversityofCalifornia,Irvine,CA,USA FriedemannMattern ETHZurich,Switzerland JohnC.Mitchell StanfordUniversity,CA,USA MoniNaor WeizmannInstituteofScience,Rehovot,Israel OscarNierstrasz UniversityofBern,Switzerland C.PanduRangan IndianInstituteofTechnology,Madras,India BernhardSteffen TUDortmundUniversity,Germany MadhuSudan MicrosoftResearch,Cambridge,MA,USA DemetriTerzopoulos UniversityofCalifornia,LosAngeles,CA,USA DougTygar UniversityofCalifornia,Berkeley,CA,USA GerhardWeikum MaxPlanckInstituteforInformatics,Saarbruecken,Germany Franz Winkler (Ed.) Algebraic Informatics 4th International Conference, CAI 2011 Linz, Austria, June 21-24, 2011 Proceedings 1 3 VolumeEditor FranzWinkler JohannesKeplerUniversity ResearchInstituteforSymbolicComputation(RISC) AltenbergerStraße69,4040,Linz,Austria E-mail:[email protected] ISSN0302-9743 e-ISSN1611-3349 ISBN978-3-642-21492-9 e-ISBN978-3-642-21493-6 DOI10.1007/978-3-642-21493-6 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2011928784 CRSubjectClassification(1998):F.4,I.1.3,F.1.1,F.4.1,F.4.3,F.4.2 LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues ©Springer-VerlagBerlinHeidelberg2011 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting, reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965, initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable toprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Typesetting:Camera-readybyauthor,dataconversionbyScientificPublishingServices,Chennai,India Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface CAI 2011 was the 4th International Conference on Algebraic Informatics. The three previous conferences, CAI 2005, CAI 2007, and CAI 2009, were all held at the Department of Mathematics of the Aristotle University of Thessaloniki in Greece. At CAI 2009, the Steering Committee asked me to organize CAI 2011 at RISC in Linz/Hagenberg, Austria; a proposal which I gladly accepted. In fact the focus of CAI is in very close correlation to the research topics at RISC,seeingmathematicsandcomputerscienceasoneacademicfieldwithclose internal interactions and mutual dependencies. Thus, CAI 2011 continued the tradition established by previous CAIs, namely, to bring together researchers from theoretical computer science and constructive algebra. The goal of this endeavorwas to enhance the understanding of syntactic and semantic problems byalgebraicmodels;andalsotopropagatetheapplicationofmoderntechniques frominformaticsinalgebraiccomputation.CAI2011triedtoachievethesegoals via invited lectures, tutorials, and contributed research talks. As stated in the call for papers and on the homepage of CAI 2011, the topics of interest included algebraic semantics, formal power series, syntactic objects,algebraicpicture processing,finite and infinite computations,acceptors and transducers for discrete structures, decision problems, algebraic characteri- zationoflogicaltheories,processalgebra,algebraicalgorithms,algebraiccoding theory, algebraic aspects of cryptography, term rewriting, algebraic aspects of number theory. The programof CAI 2011 consisted of 4 invited lectures and 13 contributed talks. With 1 exception, all these presentations are reflected in the proceed- ings. Additionally 2 tutorials were given: by A. Middeldorp and F. Neurauter on “Termination and Complexity of Rewrite Systems,” and by P. Padawitz on “Co/Algebraic Modelling and Verification at Work.” Unfortunatey, during the preparation phase of CAI 2011 one of our leading colleagues and designated memberoftheProgramCommittee,StephenL.Bloom,passedaway.Inthefirst lectureattheopeningofCAI2011,Z.E´sik,memberoftheSteeringCommittee, recalled the life and academic achievements of Stephen L. Bloom. IamgratefultoagreatnumberofcolleaguesformakingCAI2011asuccessful event: the members of the Steering Committee, the colleagues in the Program Committee, my co-workers in the Local Committee, and also Alfred Hofmann and his team at Springer LNCS. June 2011 Franz Winkler Organization CAI 2011 was organized by the Research Institute for Symbolic Computation, Johannes Kepler University Linz. Steering Committee Jean Berstel, Marne-la-Vall´ee Symeon Bozapalidis, Thessaloniki Zolt´an E´sik, Szeged Werner Kuich, Vienna Arto Salomaa, Turku Program Committee Erhard Aichinger, Linz Armin Biere, Linz Symeon Bozapalidis, Thessaloniki Bruno Courcelle, Bordeaux Wan Fokkink, Amsterdam Zolt´an Fu¨lo¨p, Szeged Ulrike Golas, Berlin Kevin Hammond, St. Andrews Sˇtˇepˇan Holub, Prague Jan Willem Klop, Amsterdam Barbara Ko¨nig, Duisburg Laura Kova´cs, Vienna Salvador Lucas, Valencia Damian Niwinski, Warsaw Attila Petho˝, Debrecen George Rahonis, Thessaloniki Simona Ronchi Della Rocca, Turin Davide Sangiorgi, Bologna Wolfgang Schreiner, Linz Mikhail Volkov, Ekaterinburg Franz Winkler, Linz (Chair) VIII Organization Referees E. Aichinger B. Ko¨nig A. Biere E. Kopczynski Y. Bilu L. Kova´cs E. Bonelli A. Kreuzer S. Bozapalidis S. Lucas L. Braud A. Mahboubi A. Cano D. Masulovic B. Courcelle O. Matz U. De Liguoro T. Mossakowski M. Deneufchaˆtel D. Niwinski A. Di Bucchianico K. Ogata C. Do¨nch A. Petho˝ W. Fokkink M. Pradella Z. Fu¨lo¨p P. Prihoda J. Fuss G. Rahonis S. Galbraith E. Rodr´ıguez Carbonell D. Giammarresi S. Ronchi Della Rocca U. Golas D. Sangiorgi A. Griggio W. Schreiner Y. Guiraud S. Sheinvald K. Hammond I. Shparlinski Sˇ. Holub Y. Stamatiou A. Kalampakas E. Teske-Wilson T. Kazana E. Verbeek W.-F. Ke M. Volkov M. Klazar F. Winkler J.W. Klop Organizing Committee Christian Do¨nch Franz Lichtenberger Johannes Middeke Chaˆu Ngoˆ Wolfgang Schreiner Franz Winkler (Chair) Sponsors Bundesministerium fu¨r Wissenschaft und Forschung (BMWF) Johannes Kepler Universita¨t Linz (JKU) Linzer Hochschulfonds (LHF) Land Ober¨osterreich Table of Contents Invited Papers Joint Spectral Radius Theory for Automated Complexity Analysis of Rewrite Systems ................................................. 1 Aart Middeldorp, Georg Moser, Friedrich Neurauter, Johannes Waldmann, and Harald Zankl From Grammars and Automata to Algebras and Coalgebras........... 21 Peter Padawitz Theme and Variations on the Concatenation Product................. 44 Jean-E´ric Pin Some Combinatorial Applications of Gro¨bner Bases .................. 65 Lajos R´onyai and Tama´s M´esza´ros Contributed Papers Comparing Necessary Conditions for Recognizability of Two-dimensional Languages....................................... 84 Marcella Anselmo and Maria Madonia Typed Monoids – An Eilenberg-Like Theorem for Non Regular Languages ...................................................... 97 Christoph Behle, Andreas Krebs, and Stephanie Reifferscheid Codes and CombinatorialStructures from Circular Planar Nearrings ... 115 Anna Benini, Achille Frigeri, and Fiorenza Morini Independence of Hyperlogarithms over Function Fields via Algebraic Combinatorics................................................... 127 Matthieu Deneufchaˆtel, G´erard H.E. Duchamp, Vincel Hoang Ngoc Minh, and Allan I. Solomon Quantifier Elimination over Finite Fields Using Gro¨bner Bases......... 140 Sicun Gao, Andr´e Platzer, and Edmund M. Clarke F-Rank-Width of (Edge-Colored)Graphs ........................... 158 Mamadou Moustapha Kant´e and Michael Rao An Algorithm for Computing a Basis of a Finite Abelian Group ....... 174 Gregory Karagiorgos and Dimitrios Poulakis X Table of Contents Rewriting in Varieties of Idempotent Semigroups..................... 185 Ondˇrej Kl´ıma, Miroslav Korbela´ˇr, and Libor Pola´k Simplifying Algebraic Functional Systems ........................... 201 Cynthia Kop Hadamard Matrices, Designs and Their Secret-Sharing Schemes........ 216 Christos Koukouvinos, Dimitris E. Simos, and Zlatko Varbanov I-RiSC: An SMT-Compliant Solver for the Existential Fragment of Real Algebra .................................................... 230 Ulrich Loup and Erika A´brah´am Variable Tree Automata over Infinite Ranked Alphabets .............. 247 Irini-Eleftheria Mens and George Rahonis Author Index.................................................. 261 Joint Spectral Radius Theory for Automated (cid:2) Complexity Analysis of Rewrite Systems Aart Middeldorp1, Georg Moser1, Friedrich Neurauter1, Johannes Waldmann2, and Harald Zankl1 1 Instituteof Computer Science, Universityof Innsbruck,Austria 2 Fakult¨at Informatik, Mathematik undNaturwissenschaften, Hochschule fu¨r Technik,Wirtschaft undKulturLeipzig, Germany Abstract. Matrixinterpretationscanbeusedtoboundthederivational complexity of term rewrite systems. In particular, triangular matrix in- terpretations overthenatural numbersare known toinducepolynomial upper bounds on the derivational complexity of (compatible) rewrite systems. Recently two different improvements were proposed, based on the theory of weighted automata and linear algebra. In this paper we strengthen and unify these improvements by using joint spectral radius theory. Keywords: derivational complexity, matrix interpretations, weighted automata, joint spectral radius. 1 Introduction This paper is concerned with automated complexity analysis of term rewrite systems. Given a terminating rewrite system, the aim is to obtain information about the maximal length of rewrite sequences in terms of the size of the initial term. This is knownas derivationalcomplexity. Developing methods for bound- ing the derivational complexity of rewrite systems has become an active and competitive1 researcharea in the past few years (e.g. [6, 11–15, 19, 21]). Matrix interpretations [4] are a popular method for automatically proving termination of rewrite systems. They can readily be used to establish upper bounds on the derivational complexity of compatible rewrite systems. However, in general, matrix interpretations induce exponential (rather than polynomial) upperbounds.Inordertoobtainpolynomialupperbounds,thematricesusedin a matrix interpretation must satisfy certain (additional) restrictions, the study of which is the central concern of [14, 15, 19]. So what are the conditions for polynomial boundedness of a matrix inter- pretation? In the literature,two different approacheshave emerged. On the one hand,thereistheautomata-basedapproachof[19],wherematricesareviewedas (cid:2) This research is supported by FWF (Austrian Science Fund) project P20133. Friedrich Neurauter is supported by a grant of theUniversity of Innsbruck. 1 http://www.termination-portal.org/wiki/Complexity F.Winkler(Ed.):CAI2011,LNCS6742,pp.1–20,2011. (cid:2)c Springer-VerlagBerlinHeidelberg2011 2 A. Middeldorp et al. weighted(word)automatacomputinga weightfunction,whichisrequiredtobe polynomially bounded. The resultis a complete characterization(i.e., necessary and sufficient conditions) of polynomially bounded matrix interpretations over N. On the other hand, there is the algebraic approachpursued in [15] (originat- ing from[14]) thatcanhandle matrix interpretationsoverN,Q,andR but only provides sufficient conditions for polynomial boundedness. In what follows, we shall see, however,that these two seemingly different approaches can be unified and strengthened with the help of joint spectral radius theory [9, 10], a branch of mathematics dedicated to studying the growth rate of products of matrices taken from a set. Theremainderofthis paperisorganizedasfollows.Inthenextsectionwere- callpreliminariesfromlinearalgebraandtermrewriting.Wegiveabriefaccount of the matrix method for proving termination of rewrite systems. In Section 3 weintroducethealgebraicapproachforcharacterizingthe polynomialgrowthof matrix interpretations. We improve upon the results of [15] by considering the minimal polynomial associated with the component-wise maximum matrix of the interpretation. We further show that the joint spectral radius of the matri- cesintheinterpretationprovidesabettercharacterizationofpolynomialgrowth and provide conditions for the decidability of the latter. Section 4 is devoted to automata-based methods for characterizing the polynomial growth of matrix interpretations. We revisit the characterization results of [19] and provide pre- cise complexity statements. In Section 5 we unify the two approaches and show that, in theory at least, the joint spectral radius theory approach subsumes the automata-based approach. Automation of the results presented in earlier sec- tions is the topic of Section 6. To this end we extend the results from [15, 19]. We also provide experimental results. We conclude with suggestions for future researchin Section 7. 2 Preliminaries As usual, we denote by N, Z, Q and R the sets of natural, integer, rational and real numbers. Given D ∈ {N,Z,Q,R} and m ∈ D, >D denotes the standard order of the respective domain and Dm abbreviates {x∈D |x(cid:2)m}. Linear Algebra: Let R be a ring (e.g., Z, Q, R). The ring of all n-dimensional squarematrices overRisdenotedbyRn×nandthepolynomial ring innindeter- minates x1,...,xn by R[x1,...,xn](cid:2). In the special case n = 1, any polynomial p ∈ R[x] can be written as p(x) = dk=0akxk for some d ∈ N. For the largest k such that ak (cid:3)=0, we call akxk the leading term of p, ak its leading coefficient and k its degree. The polynomial p is said to be monic if its leading coefficient is one. It is said to be linear, quadratic, cubic if its degree is one, two, three. IncaseRisequippedwithapartialorder(cid:2),thecomponent-wiseextensionof this orderto Rn×n is alsodenotedas(cid:2).We saythatamatrix Ais non-negative ifA(cid:2)0 anddenote the setofallnon-negativen-dimensionalsquarematricesof Zn×n by Nn×n. The n×n identity matrix is denoted by In and the n×n zero matrix is denoted by 0n. We simply write I and 0 if n is clear fromthe context.
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