Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg Hideki Yamasaki Hitotsubashi University
|
|
- Scott Reeves
- 6 years ago
- Views:
Transcription
1 CDMTCS Research Report Series A Simple Example of an ω-language Topologically Inequivalent to a Regular One Ludwig Staiger Martin-Luther-Universität Halle-Wittenerg Hideki Yamasaki Hitotsuashi University CDMTCS-9 July 2002 Centre for Discrete Mathematics and Theoretical Computer Science
2 A Simple Example of an ω-language Topologically Inequivalent to a Regular One Ludwig Staiger Martin-Luther-Universität Halle-Wittenerg Institut für Informatik von-seckendorff-platz, D Halle (Saale), Germany Electronic Mail: staiger@informatik.uni-halle.de Hideki Yamasaki Department of Mathematics, Hitotsuashi University Kunitachi, Tokyo , Japan Electronic Mail: yamasaki@math.hit-u.ac.jp Landweers s paper [La69] and the susequent ones [SW74, TY83] proved a strong relationship etween acceptance conditions imposed on finite automata on ω-words and the first classes of the Borel hierarchy in the Cantor space of all ω-words, (X ω,ρ), over a finite alphaet X. In Theorem 5 of [SW74] it is shown that an ω-language accepted y a finite automaton eing simultaneously an F σ - and a G δ -set elongs already to the Boolean closure of the class of all open (or, equivalently, closed) susets of (X ω,ρ), B(G). Thus, an ω-language F X ω which is simultaneously an F σ - and a G δ -set ut not a Boolean comination of open sets cannot e accepted y a finite automaton. For a more detailed discussion see e.g. [EH93, St97] or [Th90], for the notation used here see [St97]. The aim of this note is to provide a simple example that a proposition analogous to Theorem 5 of [SW74] is no longer true if we increase the computational power of the accepting device slightly: We augment the finite control y a so-called lind counter (cf. [EH93, Fi0], these automata are also known as partially lind counter automata [Gr78]), that is, y a counter which has no influence on the computational ehavior of the automaton except This paper was written during my visit to Institut für Informatik, Martin-Luther-Universität Halle- Wittenerg, 999, supported y grant 0-KO-87 from Ministry of Education, Culture, Sports, Science and Technology of Japan. The meaning of the word simple here is twofold: on the one hand, as explained aove, the topological complexity of our counterexample is the simplest possile one, and, on the other hand, the accepting device has a power only slightly increasing the power of a finite automaton.
3 2 L. Staiger and H. Yamasaki that the automaton gets stuck when the counter is decremented elow zero. Moreover we require the counter to e one-turn, that is, once we decrease the value of the counter we cannot increase it afterwards. We are not going to define these one-turn lind one-counter automata in full detail, instead we proceed with the announced example. On reading the first lock of a s a,+ a,±0 a,±0,±0,±0 s 0 s s 2, Figure : A Büchi automaton accepting the ω-language of Eq. () the automaton stores the lock length in the counter, and after reading the first the automaton switches to the cycle of states s,s 2 where the counter is decremented after every second. Thus the automaton gets stuck when the input a i w contains at least 2i + 2 s and, consequently, if the automaton does not get stuck it will finally stay in one of its states. (Looping etween s and s 2 is ounded y the numer of initial as.) Thus depending on the infinite input word ξ our automaton will stay in s 0, if ξ = a ω s = s, if ξ = a n ξ and ξ contains an even numer of s less than 2n + s 2, if ξ = a n ξ and ξ contains an odd numer of s less than 2n + 2. Our acceptance condition is Büchi s condition and the set of final states is {s 2 }, that is, an ω-word ξ {a,} ω is accepted if and only if the automaton runs infinitely often through state s 2 when reading ξ. Thus the ω-language accepted y our automaton is F = a n (a ) 2i+ a ω. () n N i n This ω-language is a countale suset of {a,} ω, thus an F σ -set. Since it is accepted y a deterministic automaton using Büchi acceptance it is also a G δ -suset of {a,} ω (cf. [EH93, St97]). We are going to show that our ω-language F cannot e represented as a Boolean comination of open (or closed) ω-languages. Thus, according to Theorem 5 of [SW74] (an even stronger version is Corollary 23 of [St83]), it cannot e accepted y a finite automaton. Assume the contrary, that is, let E i,e i e open susets of {a,}ω such that F = k i= E i E i. (2)
4 A Simple Example 3 Consequently, every suset F w {a,} ω has a similar representation F w {a,} ω = k i= ( Ei w {a,} ω) ( E i w {a,} ω). (3) as a Boolean comination of open sets E i w {a,} ω and E i w {a,}ω. Consider the ω-languages F n := F a n {a,} ω = a n i n (a ) 2i+ a ω. Every single ω-language F n is accepted y a finite automaton. Moreover, F n is essentially (up to the prefix a n and the encoding: a and 0 ) Wagner s ω-language c 2n := i<n (a ) 2i+ a ω taken over the alphaet {a,}. It is shown in Lemma of [Wa79] that c 2n+ Ĉ 2n+ Ĉ 2n and, consequently, F n Ĉ 2n Ĉ 2n 3. For the definition of Wagner classes see [Wa79, p. 39] or Definition 4. of [St97]. At the same time Eq. (3) and the fact that the ω-languages F n are accepted y finite automata imply F n Ĉ 2k+ for all n N, a contradiction. Thus Eqs. (3) and (2) cannot hold true, and F is not a Boolean comination of open susets of Cantor space (X ω,ρ). Finally, we present the Petri net derived from the automaton in Fig. which accepts the same ω-language. For acceptance of ω-languages y Petri nets see [HR86, Va83]. a a a Figure 2: A Petri net accepting F In Fig. 2, the initial marking is represented y a lack dot. We also adopt Büchi s acceptance condition with the set of accepting markings having at least one token in the douly circled place. Likewise we may adopt the co-büchi acceptance condition where ultimately all accepting markings have a token in the douly circled place.
5 4 L. Staiger and H. Yamasaki References [EH93] [Fi0] J.Engelfriet and H.J. Hoogeoom, X-automata on ω-words, Theoret. Comput. Sci. 0 (993), 5. O. Finkel, Wadge hierarchy of omega context-free languages. Theoret. Comput. Sci. 269 (200), [La69] L.H. Landweer, Decision prolems for ω-automata, Math. Syst. Theory 3 (969) 4, [Gr78] [HR86] S. Greiach. Remarks on lind and partially lind one-way multicounter machines. Theoret. Comput. Sci. 7 (978), H.J. Hoogeoom and G. Rozenerg, Infinitary languages: Basic theory and applications to concurrent systems. In: Current Trends in Concurrency. Overviews and Tutorials (eds. J.W. de Bakker, W.-P. de Roever and G. Rozenerg), Lect. Notes Comput. Sci. 224, Springer-Verlag, Berlin 986, [St83] L. Staiger, Finite-state ω-languages. J. Comput. System Sci. 27 (983) 3, [St97] L. Staiger, ω-languages, in: Handook of Formal Languages, Vol. 3, G. Rozenerg and A. Salomaa (Eds.), Springer-Verlag, Berlin 997, [SW74] [TY83] [Th90] L. Staiger und K. Wagner, Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen. Elektron. Informationsverar. Kyernetik EIK 0 (974) 7, M. Takahashi and H. Yamasaki, A note on ω-regular languages. Theoret. Comput. Sci. 23 (983), W. Thomas, Automata on infinite ojects, in: Handook of Theoretical Computer Science, Vol. B, J. Van Leeuwen (Ed.), Elsevier, Amsterdam 990, [Va83] R. Valk, Infinite ehaviour of Petri nets. Theoret. Comput. Sci. 25 (983), [Wa79] K. Wagner, On ω-regular sets. Inform. and Control 43 (979),
Topologies refining the CANTOR topology on X ω
CDMTCS Research Report Series Topologies refining the CANTOR topology on X ω Sibylle Schwarz Westsächsische Hochschule Zwickau Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg CDMTCS-385 June
More informationAcceptance of!-languages by Communicating Deterministic Turing Machines
Acceptance of!-languages by Communicating Deterministic Turing Machines Rudolf Freund Institut für Computersprachen, Technische Universität Wien, Karlsplatz 13 A-1040 Wien, Austria Ludwig Staiger y Institut
More informationEfficient minimization of deterministic weak ω-automata
Information Processing Letters 79 (2001) 105 109 Efficient minimization of deterministic weak ω-automata Christof Löding Lehrstuhl Informatik VII, RWTH Aachen, 52056 Aachen, Germany Received 26 April 2000;
More informationStefan Hoffmann Universität Trier Sibylle Schwarz HTWK Leipzig Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg
CDMTCS Research Report Series Shift-Invariant Topologies for the Cantor Space X ω Stefan Hoffmann Universität Trier Sibylle Schwarz HTWK Leipzig Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg
More informationOn the Accepting Power of 2-Tape Büchi Automata
On the Accepting Power of 2-Tape Büchi Automata Equipe de Logique Mathématique Université Paris 7 STACS 2006 Acceptance of infinite words In the sixties, Acceptance of infinite words by finite automata
More informationCDMTCS Research Report Series. The Maximal Subword Complexity of Quasiperiodic Infinite Words. Ronny Polley 1 and Ludwig Staiger 2.
CDMTCS Research Report Series The Maximal Subword Complexity of Quasiperiodic Infinite Words Ronny Polley 1 and Ludwig Staiger 2 1 itcampus Software- und Systemhaus GmbH, Leipzig 2 Martin-Luther-Universität
More informationarxiv: v2 [cs.lo] 26 Mar 2018
Wadge Degrees of ω-languages of Petri Nets Olivier Finkel Equipe de Logique Mathématique Institut de Mathématiques de Jussieu - Paris Rive Gauche CNRS et Université Paris 7, France. finkel@math.univ-paris-diderot.fr
More informationCDMTCS Research Report Series. The Kolmogorov complexity of infinite words. Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg
CDMTCS Research Report Series The Kolmogorov complexity of infinite words Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg CDMTCS-279 May 2006 Centre for Discrete Mathematics and Theoretical Computer
More informationCDMTCS Research Report Series. Quasiperiods, Subword Complexity and the Smallest Pisot Number
CDMTCS Research Report Series Quasiperiods, Subword Complexity and the Smallest Pisot Number Ronny Polley itcampus Software- und Systemhaus GmbH, Leipzig Ludwig Staiger Martin-Luther-Universität Halle-Wittenberg
More informationReversal of regular languages and state complexity
Reversal of regular languages and state complexity Juraj Šeej Institute of Computer Science, Faculty of Science, P. J. Šafárik University Jesenná 5, 04001 Košice, Slovakia juraj.seej@gmail.com Astract.
More informationLanguages. A language is a set of strings. String: A sequence of letters. Examples: cat, dog, house, Defined over an alphabet:
Languages 1 Languages A language is a set of strings String: A sequence of letters Examples: cat, dog, house, Defined over an alphaet: a,, c,, z 2 Alphaets and Strings We will use small alphaets: Strings
More informationWatson-Crick ω-automata. Elena Petre. Turku Centre for Computer Science. TUCS Technical Reports
Watson-Crick ω-automata Elena Petre Turku Centre for Computer Science TUCS Technical Reports No 475, December 2002 Watson-Crick ω-automata Elena Petre Department of Mathematics, University of Turku and
More informationThe Wadge Hierarchy of Deterministic Tree Languages
The Wadge Hierarchy of Deterministic Tree Languages Filip Murlak Institute of Informatics, Warsaw University ul. Banacha 2, 02 097 Warszawa, Poland fmurlak@mimuw.edu.pl Abstract. We provide a complete
More informationAutomata, Logic and Games: Theory and Application
Automata, Logic and Games: Theory and Application 2 Parity Games, Tree Automata, and S2S Luke Ong University of Oxford TACL Summer School University of Salerno, 14-19 June 2015 Luke Ong S2S 14-19 June
More informationarxiv: v1 [math.lo] 10 Sep 2018
An Effective Property of ω-rational Functions Olivier Finkel arxiv:1809.03220v1 [math.lo] 10 Sep 2018 Institut de Mathématiques de Jussieu - Paris Rive Gauche CNRS et Université Paris 7, France. Olivier.Finkel@math.univ-paris-diderot.fr
More informationLevel Two of the quantifier alternation hierarchy over infinite words
Loughborough University Institutional Repository Level Two of the quantifier alternation hierarchy over infinite words This item was submitted to Loughborough University's Institutional Repository by the/an
More informationFinite Automata and Regular Languages (part II)
Finite Automata and Regular Languages (part II) Prof. Dan A. Simovici UMB 1 / 25 Outline 1 Nondeterministic Automata 2 / 25 Definition A nondeterministic finite automaton (ndfa) is a quintuple M = (A,
More informationIntroduction. Büchi Automata and Model Checking. Outline. Büchi Automata. The simplest computation model for infinite behaviors is the
Introduction Büchi Automata and Model Checking Yih-Kuen Tsay Department of Information Management National Taiwan University FLOLAC 2009 The simplest computation model for finite behaviors is the finite
More informationLogic and Automata I. Wolfgang Thomas. EATCS School, Telc, July 2014
Logic and Automata I EATCS School, Telc, July 2014 The Plan We present automata theory as a tool to make logic effective. Four parts: 1. Some history 2. Automata on infinite words First step: MSO-logic
More informationIncompleteness Theorems, Large Cardinals, and Automata ov
Incompleteness Theorems, Large Cardinals, and Automata over Finite Words Equipe de Logique Mathématique Institut de Mathématiques de Jussieu - Paris Rive Gauche CNRS and Université Paris 7 TAMC 2017, Berne
More informationRepresenting Arithmetic Constraints with Finite Automata: An Overview
Representing Arithmetic Constraints with Finite Automata: An Overview Bernard Boigelot Pierre Wolper Université de Liège Motivation Linear numerical constraints are a very common and useful formalism (our
More informationWADGE HIERARCHY OF OMEGA CONTEXT FREE LANGUAGES
WADGE HIERARCHY OF OMEGA CONTEXT FREE LANGUAGES Olivier Finkel Equipe de Logique Mathématique CNRS URA 753 et Université Paris 7 U.F.R. de Mathématiques 2 Place Jussieu 75251 Paris cedex 05, France. E
More informationVIC 2004 p.1/26. Institut für Informatik Universität Heidelberg. Wolfgang Merkle and Jan Reimann. Borel Normality, Automata, and Complexity
Borel Normality, Automata, and Complexity Wolfgang Merkle and Jan Reimann Institut für Informatik Universität Heidelberg VIC 2004 p.1/26 The Quest for Randomness Intuition: An infinite sequence of fair
More informationAutomata-based Verification - III
COMP30172: Advanced Algorithms Automata-based Verification - III Howard Barringer Room KB2.20: email: howard.barringer@manchester.ac.uk March 2009 Third Topic Infinite Word Automata Motivation Büchi Automata
More informationOn Recognizable Languages of Infinite Pictures
On Recognizable Languages of Infinite Pictures Equipe de Logique Mathématique CNRS and Université Paris 7 JAF 28, Fontainebleau, Juin 2009 Pictures Pictures are two-dimensional words. Let Σ be a finite
More informationOn Stateless Multicounter Machines
On Stateless Multicounter Machines Ömer Eğecioğlu and Oscar H. Ibarra Department of Computer Science University of California, Santa Barbara, CA 93106, USA Email: {omer, ibarra}@cs.ucsb.edu Abstract. We
More informationThe WHILE Hierarchy of Program Schemes is Infinite
The WHILE Hierarchy of Program Schemes is Infinite Can Adam Alayrak and Thomas Noll RWTH Aachen Ahornstr. 55, 52056 Aachen, Germany alayrak@informatik.rwth-aachen.de and noll@informatik.rwth-aachen.de
More informationOn decision problems for timed automata
On decision problems for timed automata Olivier Finkel Equipe de Logique Mathématique, U.F.R. de Mathématiques, Université Paris 7 2 Place Jussieu 75251 Paris cedex 05, France. finkel@logique.jussieu.fr
More informationOn the Continuity Set of an omega Rational Function
On the Continuity Set of an omega Rational Function Olivier Carton, Olivier Finkel, Pierre Simonnet To cite this version: Olivier Carton, Olivier Finkel, Pierre Simonnet. On the Continuity Set of an omega
More informationInference of ω-languages from Prefixes
Inference of ω-languages from Prefixes Colin DE LA HIGUERA and Jean-Christophe JANODET EURISE, Université de Saint-Etienne France cdlh@univ-st-etienne.fr, janodet@univ-st-etienne.fr Astract. Büchi automata
More informationSubsumption of concepts in FL 0 for (cyclic) terminologies with respect to descriptive semantics is PSPACE-complete.
Subsumption of concepts in FL 0 for (cyclic) terminologies with respect to descriptive semantics is PSPACE-complete. Yevgeny Kazakov and Hans de Nivelle MPI für Informatik, Saarbrücken, Germany E-mail:
More informationThe Emptiness Problem for Valence Automata or: Another Decidable Extension of Petri Nets
The Emptiness Problem for Valence Automata or: Another Decidable Extension of Petri Nets Georg Zetzsche Technische Universität Kaiserslautern Reachability Problems 2015 Georg Zetzsche (TU KL) Emptiness
More informationBüchi Automata and Their Determinization
Büchi Automata and Their Determinization Edinburgh, October 215 Plan of the Day 1. Büchi automata and their determinization 2. Infinite games 3. Rabin s Tree Theorem 4. Decidability of monadic theories
More informationRecognizing Tautology by a Deterministic Algorithm Whose While-loop s Execution Time Is Bounded by Forcing. Toshio Suzuki
Recognizing Tautology by a Deterministic Algorithm Whose While-loop s Execution Time Is Bounded by Forcing Toshio Suzui Osaa Prefecture University Saai, Osaa 599-8531, Japan suzui@mi.cias.osaafu-u.ac.jp
More informationP Finite Automata and Regular Languages over Countably Infinite Alphabets
P Finite Automata and Regular Languages over Countably Infinite Alphabets Jürgen Dassow 1 and György Vaszil 2 1 Otto-von-Guericke-Universität Magdeburg Fakultät für Informatik PSF 4120, D-39016 Magdeburg,
More informationOn Decision Problems for Probabilistic Büchi Automata
On Decision Prolems for Proailistic Büchi Automata Christel Baier 1, Nathalie Bertrand 2, Marcus Größer 1 1 TU Dresden, Germany 2 IRISA, INRIA Rennes, France Cachan 05 février 2008 Séminaire LSV 05/02/08,
More informationAutomata-based Verification - III
CS3172: Advanced Algorithms Automata-based Verification - III Howard Barringer Room KB2.20/22: email: howard.barringer@manchester.ac.uk March 2005 Third Topic Infinite Word Automata Motivation Büchi Automata
More informationOn Recognizable Languages of Infinite Pictures
On Recognizable Languages of Infinite Pictures Equipe de Logique Mathématique CNRS and Université Paris 7 LIF, Marseille, Avril 2009 Pictures Pictures are two-dimensional words. Let Σ be a finite alphabet
More informationComputer Sciences Department
1 Reference Book: INTRODUCTION TO THE THEORY OF COMPUTATION, SECOND EDITION, by: MICHAEL SIPSER 3 objectives Finite automaton Infinite automaton Formal definition State diagram Regular and Non-regular
More informationarxiv: v1 [cs.fl] 4 Feb 2013
Incomplete Transition Complexity of Basic Operations on Finite Languages Eva Maia, Nelma Moreira, Rogério Reis arxiv:1302.0750v1 [cs.fl] 4 Fe 2013 CMUP & DCC, Faculdade de Ciências da Universidade do Porto
More informationDefining Fairness. Paderborn, Germany
Defining Fairness Hagen Völzer a, Daniele Varacca b, and Ekkart Kindler c a University of Lübeck, Germany, b Imperial College London, UK, c University of Paderborn, Germany Abstract. We propose a definition
More informationClick to edit. Master title. style
Query Learning of Derived ω-tree Languages in Polynomial Time Dana Angluin, Tımos Antonopoulos & Dana 1 Query Learning a set of possile concepts Question Answer tc Learner Teacher Tries to identify a target
More information#A50 INTEGERS 14 (2014) ON RATS SEQUENCES IN GENERAL BASES
#A50 INTEGERS 14 (014) ON RATS SEQUENCES IN GENERAL BASES Johann Thiel Dept. of Mathematics, New York City College of Technology, Brooklyn, New York jthiel@citytech.cuny.edu Received: 6/11/13, Revised:
More informationThe State Explosion Problem
The State Explosion Problem Martin Kot August 16, 2003 1 Introduction One from main approaches to checking correctness of a concurrent system are state space methods. They are suitable for automatic analysis
More informationMonadic Second Order Logic and Automata on Infinite Words: Büchi s Theorem
Monadic Second Order Logic and Automata on Infinite Words: Büchi s Theorem R. Dustin Wehr December 18, 2007 Büchi s theorem establishes the equivalence of the satisfiability relation for monadic second-order
More informationReal-Time Systems. Lecture 15: The Universality Problem for TBA Dr. Bernd Westphal. Albert-Ludwigs-Universität Freiburg, Germany
Real-Time Systems Lecture 15: The Universality Problem for TBA 2013-06-26 15 2013-06-26 main Dr. Bernd Westphal Albert-Ludwigs-Universität Freiburg, Germany Contents & Goals Last Lecture: Extended Timed
More informationDecision Problems for Deterministic Pushdown Automata on Infinite Words
Decision Problems for Deterministic Pushdown Automata on Infinite Words Christof Löding Lehrstuhl Informatik 7 RWTH Aachen University Germany loeding@cs.rwth-aachen.de The article surveys some decidability
More informationCS256/Spring 2008 Lecture #11 Zohar Manna. Beyond Temporal Logics
CS256/Spring 2008 Lecture #11 Zohar Manna Beyond Temporal Logics Temporal logic expresses properties of infinite sequences of states, but there are interesting properties that cannot be expressed, e.g.,
More informationPumping for Ordinal-Automatic Structures *
Computability 1 (2012) 1 40 DOI IOS Press 1 Pumping for Ordinal-Automatic Structures * Martin Huschenbett Institut für Informatik, Ludwig-Maximilians-Universität München, Germany martin.huschenbett@ifi.lmu.de
More informationThe exact complexity of the infinite Post Correspondence Problem
The exact complexity of the infinite Post Correspondence Problem Olivier Finkel To cite this version: Olivier Finkel. The exact complexity of the infinite Post Correspondence Problem. Information Processing
More informationWeak Alternating Timed Automata
Weak Alternating Timed Automata Pawel Parys 1 and Igor Walukiewicz 2 1 Warsaw University,Poland 2 LaBRI, CNRS and Bordeaux University, France Abstract. Alternating timed automata on infinite words are
More informationTree Automata and Rewriting
and Rewriting Ralf Treinen Université Paris Diderot UFR Informatique Laboratoire Preuves, Programmes et Systèmes treinen@pps.jussieu.fr July 23, 2010 What are? Definition Tree Automaton A tree automaton
More informationThe Non-Deterministic Mostowski Hierarchy and Distance-Parity Automata
The Non-Deterministic Mostowski Hierarchy and Distance-Parity Automata Thomas Colcombet 1, and Christof Löding 2 1 LIAFA/CNRS, France 2 RWTH Aachen, Germany Abstract. Given a Rabin tree-language and natural
More informationValence automata as a generalization of automata with storage
Valence automata as a generalization of automata with storage Georg Zetzsche Technische Universität Kaiserslautern D-CON 2013 Georg Zetzsche (TU KL) Valence automata D-CON 2013 1 / 23 Example (Pushdown
More informationUnit 6. Non Regular Languages The Pumping Lemma. Reading: Sipser, chapter 1
Unit 6 Non Regular Languages The Pumping Lemma Reading: Sipser, chapter 1 1 Are all languages regular? No! Most of the languages are not regular! Why? A finite automaton has limited memory. How can we
More informationDefinition of Büchi Automata
Büchi Automata Definition of Büchi Automata Let Σ = {a,b,...} be a finite alphabet. By Σ ω we denote the set of all infinite words over Σ. A non-deterministic Büchi automaton (NBA) over Σ is a tuple A
More informationTWO TO ONE IMAGES AND PFA
TWO TO ONE IMAGES AND PFA ALAN DOW Astract. We prove that all maps on N that are exactly two to one are trivial if PFA is assumed. 1. Introduction A map f : X K is precisely two to one if for each k K,
More informationComplexity of infinite tree languages
Complexity of infinite tree languages when automata meet topology Damian Niwiński University of Warsaw joint work with André Arnold, Szczepan Hummel, and Henryk Michalewski Liverpool, October 2010 1 Example
More informationIntroduction to weighted automata theory
Introduction to weighted automata theory Lectures given at the 19th Estonian Winter School in Computer Science Jacques Sakarovitch CNRS / Telecom ParisTech Based on Chapter III Chapter 4 The presentation
More informationFinite Automata. Mahesh Viswanathan
Finite Automata Mahesh Viswanathan In this lecture, we will consider different models of finite state machines and study their relative power. These notes assume that the reader is familiar with DFAs,
More informationSri vidya college of engineering and technology
Unit I FINITE AUTOMATA 1. Define hypothesis. The formal proof can be using deductive proof and inductive proof. The deductive proof consists of sequence of statements given with logical reasoning in order
More informationLTL is Closed Under Topological Closure
LTL is Closed Under Topological Closure Grgur Petric Maretić, Mohammad Torabi Dashti, David Basin Department of Computer Science, ETH Universitätstrasse 6 Zürich, Switzerland Abstract We constructively
More informationMANFRED DROSTE AND WERNER KUICH
Logical Methods in Computer Science Vol. 14(1:21)2018, pp. 1 14 https://lmcs.episciences.org/ Submitted Jan. 31, 2017 Published Mar. 06, 2018 WEIGHTED ω-restricted ONE-COUNTER AUTOMATA Universität Leipzig,
More informationRecursion and Topology on 2 ω for Possibly Infinite Computations. Verónica Becher Departamento de Computación, Universidad de Buenos Aires, Argentina
Recursion and Topology on 2 ω for Possibly Infinite Computations Verónica Becher Departamento de Computación, Universidad de Buenos Aires, Argentina vbecher@dc.uba.ar Serge Grigorieff LIAFA, Université
More informationDeterministic ω-automata for LTL: A safraless, compositional, and mechanically verified construction
Deterministic ω-automata for LTL: A safraless, compositional, and mechanically verified construction Javier Esparza 1 Jan Křetínský 2 Salomon Sickert 1 1 Fakultät für Informatik, Technische Universität
More informationTopological extension of parity automata
Topological extension of parity automata Micha l Skrzypczak University of Warsaw Institute of Informatics Banacha 2 02-097 Warsaw, Poland Abstract The paper presents a concept of a coloring an extension
More informationFinitary Winning in \omega-regular Games
Finitary Winning in \omega-regular Games Krishnendu Chatterjee Thomas A. Henzinger Florian Horn Electrical Engineering and Computer Sciences University of California at Berkeley Technical Report No. UCB/EECS-2007-120
More informationPlan for Today and Beginning Next week (Lexical Analysis)
Plan for Today and Beginning Next week (Lexical Analysis) Regular Expressions Finite State Machines DFAs: Deterministic Finite Automata Complications NFAs: Non Deterministic Finite State Automata From
More informationAnalysis and Optimization of Discrete Event Systems using Petri Nets
Volume 113 No. 11 2017, 1 10 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu Analysis and Optimization of Discrete Event Systems using Petri Nets
More informationDiscrete Event Systems Exam
Computer Engineering and Networks Laboratory TEC, NSG, DISCO HS 2016 Prof. L. Thiele, Prof. L. Vanbever, Prof. R. Wattenhofer Discrete Event Systems Exam Friday, 3 rd February 2017, 14:00 16:00. Do not
More informationEXTERNAL AUTOMORPHISMS OF ULTRAPRODUCTS OF FINITE MODELS
EXTERNAL AUTOMORPHISMS OF ULTRAPRODUCTS OF FINITE MODELS PHILIPP LÜCKE AND SAHARON SHELAH Abstract. Let L be a finite first-order language and M n n < ω be a sequence of finite L-models containing models
More informationDeciding the weak definability of Büchi definable tree languages
Deciding the weak definability of Büchi definable tree languages Thomas Colcombet 1,DenisKuperberg 1, Christof Löding 2, Michael Vanden Boom 3 1 CNRS and LIAFA, Université Paris Diderot, France 2 Informatik
More informationRandom Reals à la Chaitin with or without prefix-freeness
Random Reals à la Chaitin with or without prefix-freeness Verónica Becher Departamento de Computación, FCEyN Universidad de Buenos Aires - CONICET Argentina vbecher@dc.uba.ar Serge Grigorieff LIAFA, Université
More informationOn the expressive power of existential quantification in polynomial-time computability (Extended abstract)
On the expressive power of existential quantification in polynomial-time computability (Extended abstract) Dieter Spreen Fachbereich Mathematik, Theoretische Informatik Universität Siegen, 57068 Siegen,
More informationTimo Latvala. March 7, 2004
Reactive Systems: Safety, Liveness, and Fairness Timo Latvala March 7, 2004 Reactive Systems: Safety, Liveness, and Fairness 14-1 Safety Safety properties are a very useful subclass of specifications.
More informationTHE LENGTH OF THE FULL HIERARCHY OF NORMS
Rend. Sem. Mat. Univ. Pol. Torino - Vol. 63, 2 (2005) B. Löwe THE LENGTH OF THE FULL HIERARCHY OF NORMS Abstract. We give upper and lower bounds for the length of the Full Hierarchy of Norms. 1. Introduction
More informationApplied Computer Science II Chapter 1 : Regular Languages
Applied Computer Science II Chapter 1 : Regular Languages Prof. Dr. Luc De Raedt Institut für Informatik Albert-Ludwigs Universität Freiburg Germany Overview Deterministic finite automata Regular languages
More informationLogic and Games SS 2009
Logic and Games SS 2009 Prof. Dr. Erich Grädel Łukasz Kaiser, Tobias Ganzow Mathematische Grundlagen der Informatik RWTH Aachen c b n d This work is licensed under: http://creativecommons.org/licenses/by-nc-nd/3.0/de/
More informationReversal-Bounded Counter Machines Revisited
Reversal-Bounded Counter Machines Revisited Alain Finkel 1 and Arnaud Sangnier 1,2 1 LSV, ENS Cachan, CNRS & 2 EDF R&D 61 av. du pdt Wilson 94230 Cachan. France {finkel,sangnier}@lsv.ens-cachan.fr Abstract.
More informationProperties of Languages with Catenation and
Properties of Languages with Catenation and Shuffle Nils Erik Flick and Manfred Kudlek Fachbereich Informatik, MIN-Fakultät, Universität Hamburg, DE email: {flick,kudlek}@informatik.uni-hamburg.de Abstract.
More informationCheck Character Systems Using Chevalley Groups
Designs, Codes and Cryptography, 10, 137 143 (1997) c 1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Check Character Systems Using Chevalley Groups CLAUDIA BROECKER 2. Mathematisches
More informationKybernetika. Daniel Reidenbach; Markus L. Schmid Automata with modulo counters and nondeterministic counter bounds
Kybernetika Daniel Reidenbach; Markus L. Schmid Automata with modulo counters and nondeterministic counter bounds Kybernetika, Vol. 50 (2014), No. 1, 66 94 Persistent URL: http://dml.cz/dmlcz/143764 Terms
More informationLogic Model Checking
Logic Model Checking Lecture Notes 10:18 Caltech 101b.2 January-March 2004 Course Text: The Spin Model Checker: Primer and Reference Manual Addison-Wesley 2003, ISBN 0-321-22862-6, 608 pgs. the assignment
More informationAlan Bundy. Automated Reasoning LTL Model Checking
Automated Reasoning LTL Model Checking Alan Bundy Lecture 9, page 1 Introduction So far we have looked at theorem proving Powerful, especially where good sets of rewrite rules or decision procedures have
More informationA Survey of Partial-Observation Stochastic Parity Games
Noname manuscript No. (will be inserted by the editor) A Survey of Partial-Observation Stochastic Parity Games Krishnendu Chatterjee Laurent Doyen Thomas A. Henzinger the date of receipt and acceptance
More informationOn the Borel complexity of MSO definable sets of branches
Fundamenta Informaticae XXI (2001) 1001 1013 1001 IOS Press On the Borel complexity of MSO definable sets of branches Mikołaj Bojańczyk, Damian Niwiński Institute of Informatics University of Warsaw Poland
More informationBranching Bisimilarity with Explicit Divergence
Branching Bisimilarity with Explicit Divergence Ro van Glaeek National ICT Australia, Sydney, Australia School of Computer Science and Engineering, University of New South Wales, Sydney, Australia Bas
More informationOn Modal µ-calculus And Non-Well-Founded Set Theory
On Modal µ-calculus And Non-Well-Founded Set Theory Luca Alberucci (albe@iam.unibe.ch) and Vincenzo Salipante (salipant@iam.unibe.ch) Institut für Informatik und angewandte Mathematik, Universität Bern,
More informationRED. Name: Math 290 Fall 2016 Sample Exam 3
RED Name: Math 290 Fall 2016 Sample Exam 3 Note that the first 10 questions are true false. Mark A for true, B for false. Questions 11 through 20 are multiple choice. Mark the correct answer on your ule
More informationOn Recognizable Tree Languages Beyond the Borel Hierarchy
On Recognizable Tree Languages Beyond the Borel Hierarchy Olivier Finkel, Pierre Simonnet To cite this version: Olivier Finkel, Pierre Simonnet. On Recognizable Tree Languages Beyond the Borel Hierarchy.
More informationReversal-Bounded Counter Machines
Reversal-Bounded Counter Machines Stéphane Demri LSV, CNRS, ENS Cachan Workshop on Logics for Resource-Bounded Agents, Barcelona, August 2015 Overview Presburger Counter Machines Reversal-Bounded Counter
More informationDeterministic Finite Automata
Deterministic Finite Automata COMP2600 Formal Methods for Software Engineering Ranald Clouston Australian National University Semester 2, 2013 COMP 2600 Deterministic Finite Automata 1 Pop quiz What is
More informationACS2: Decidability Decidability
Decidability Bernhard Nebel and Christian Becker-Asano 1 Overview An investigation into the solvable/decidable Decidable languages The halting problem (undecidable) 2 Decidable problems? Acceptance problem
More informationFinite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018
Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2018 Lecture 4 Ana Bove March 23rd 2018 Recap: Formal Proofs How formal should a proof be? Depends on its purpose...... but should be convincing......
More informationThe complexity of unary tiling recognizable picture languages: nondeterministic and unambiguous cases
Fundamenta Informaticae X (2) 1 20 1 IOS Press The complexity of unary tiling recognizale picture languages: nondeterministic and unamiguous cases Alerto Bertoni Massimiliano Goldwurm Violetta Lonati Dipartimento
More informationPositive varieties and infinite words
Positive varieties and infinite words Jean-Eric Pin To cite this version: Jean-Eric Pin. Positive varieties and infinite words. 1998, Springer, Berlin, pp.76-87, 1998, Lecture Notes in Comput. Sci. 1380.
More informationFinite Automata Theory and Formal Languages TMV027/DIT321 LP4 2017
Finite Automata Theory and Formal Languages TMV027/DIT321 LP4 2017 Lecture 4 Ana Bove March 24th 2017 Structural induction; Concepts of automata theory. Overview of today s lecture: Recap: Formal Proofs
More informationω-automata Automata that accept (or reject) words of infinite length. Languages of infinite words appear:
ω-automata ω-automata Automata that accept (or reject) words of infinite length. Languages of infinite words appear: in verification, as encodings of non-terminating executions of a program. in arithmetic,
More informationNon-emptiness Testing for TMs
180 5. Reducibility The proof of unsolvability of the halting problem is an example of a reduction: a way of converting problem A to problem B in such a way that a solution to problem B can be used to
More informationOn the complexity of infinite computations
On the complexity of infinite computations Damian Niwiński, Warsaw University joint work with Igor Walukiewicz and Filip Murlak Newton Institute, Cambridge, June 2006 1 Infinite computations Büchi (1960)
More information