Languages, Automata, and Logic

The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

[1]  Neil Immerman,et al.  Languages that Capture Complexity Classes , 1987, SIAM J. Comput..

[2]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs IX: Machines and their Behaviours , 1995, Theor. Comput. Sci..

[3]  Andreas Potthoff First-Order Logic on Finite Trees , 1995, TAPSOFT.

[4]  Robin Milner,et al.  Operational and Algebraic Semantics of Concurrent Processes , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[5]  Nils Klarlund,et al.  Hardware Verification using Monadic Second-Order Logic , 1995, CAV.

[6]  Bruno Courcelle,et al.  The Expression of Graph Properties and Graph Transformations in Monadic Second-Order Logic , 1997, Handbook of Graph Grammars.

[7]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs V: On Closing the Gap Between Definability and Recognizability , 1991, Theor. Comput. Sci..

[8]  E. Allen Emerson,et al.  Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[9]  Howard Straubing,et al.  Regular Languages Defined with Generalized Quanifiers , 1995, Inf. Comput..

[10]  E. Allen Emerson,et al.  The Complexity of Tree Automata and Logics of Programs , 1999, SIAM J. Comput..

[11]  M. Rabin Decidability of second-order theories and automata on infinite trees. , 1969 .

[12]  J. Richard Büchi State-Strategies for Games in F G , 1983, J. Symb. Log..

[13]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[14]  Wieslaw Zielonka,et al.  Notes on Finite Asynchronous Automata , 1987, RAIRO Theor. Informatics Appl..

[15]  Wolfgang Thomas Logical Aspects in the Study of Tree Languages , 1984, CAAP.

[16]  André Arnold,et al.  An Initial Semantics for the mu-Calculus on Trees and Rabin's Complementation Lemma , 1995, Theor. Comput. Sci..

[17]  Yuri Gurevich,et al.  Trees, automata, and games , 1982, STOC '82.

[18]  Thomas A. Henzinger,et al.  Real-Time Logics: Complexity and Expressiveness , 1993, Inf. Comput..

[19]  Grzegorz Rozenberg,et al.  Current Trends in Concurrency , 1986, Lecture Notes in Computer Science.

[20]  Richard M. Karp,et al.  Complexity of Computation , 1974 .

[21]  Richard E. Ladner,et al.  Application of Model Theoretic Games to Discrete Linear Orders and Finite Automata , 1977, Inf. Control..

[22]  Vladimir Yakhnis,et al.  Extension of Gurevich-Harrington's Restricted Memory Determinacy Theorem: A Criterion for the Winning Player and an Explicit Class of Winning Strategies , 1990, Ann. Pure Appl. Log..

[23]  Marcel Paul Schützenberger,et al.  On Finite Monoids Having Only Trivial Subgroups , 1965, Inf. Control..

[24]  Dominique Perrin,et al.  First-Order Logic and Star-Free Sets , 1986, J. Comput. Syst. Sci..

[25]  E. Allen Emerson,et al.  Automated Temporal Reasoning about Reactive Systems , 1996, Banff Higher Order Workshop.

[26]  Y. Moschovakis Descriptive Set Theory , 1980 .

[27]  Wolfgang Thomas,et al.  A Combinatorial Approach to the Theory of omega-Automata , 1981, Inf. Control..

[28]  Howard Straubing Finite Automata, Formal Logic, and Circuit Complexity , 1994, Progress in Theoretical Computer Science.

[29]  M. Rabin Weakly Definable Relations and Special Automata , 1970 .

[30]  Bruno Courcelle,et al.  The Monadic Second-Order Logic of Graphs. I. Recognizable Sets of Finite Graphs , 1990, Inf. Comput..

[31]  Ronald Fagin Generalized first-order spectra, and polynomial. time recognizable sets , 1974 .

[32]  Branislav Rovan,et al.  Mathematical Foundations of Computer Science 1994 , 1994, Lecture Notes in Computer Science.

[33]  Antonio Restivo,et al.  Two-Dimensional Languages , 1997, Handbook of Formal Languages.

[34]  Detlef Seese,et al.  Linear time computable problems and first-order descriptions , 1996, Mathematical Structures in Computer Science.

[35]  David E. Muller,et al.  Infinite sequences and finite machines , 1963, SWCT.

[36]  Orna Grumberg,et al.  Branching-Time Temporal Logic and Tree Automata , 1996, Inf. Comput..

[37]  Robert K. Brayton,et al.  Structural Complexity of Omega-Automata , 1995, STACS.

[38]  Howard Straubing,et al.  Regular Languages in NC¹ , 1992, J. Comput. Syst. Sci..

[39]  Grzegorz Rozenberg,et al.  Infinitary Languages: Basic Theory an Applications to Concurrent Systems , 1986, Current Trends in Concurrency.

[40]  Antonio Restivo,et al.  Monadic Second-Order Logic Over Rectangular Pictures and Recognizability by Tiling Systems , 1996, Inf. Comput..

[41]  Nils Klarlund,et al.  Progress measures, immediate determinacy, and a subset construction for tree automata , 1992, [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science.

[42]  David Janin,et al.  Automata for the mu-calculus and Related Results , 1995 .

[43]  Zohar Manna,et al.  The Temporal Logic of Reactive and Concurrent Systems , 1991, Springer New York.

[44]  Hendrik Jan Hoogeboom,et al.  MSO Definable Text Languages , 1994, MFCS.

[45]  Joost Engelfriet,et al.  X-Automata on omega-Words , 1993, Theor. Comput. Sci..

[46]  Jacques Sakarovitch,et al.  Synchronized Rational Relations of Finite and Infinite Words , 1993, Theor. Comput. Sci..

[47]  Sebastian Seibert Quantifier Hierarchies over Word Relations , 1991, CSL.

[48]  C. C. Elgot Decision problems of finite automata design and related arithmetics , 1961 .

[49]  Wolfgang Thomas,et al.  A hierarchy of sets of infinite trees , 1983 .

[50]  André Arnold,et al.  Finite transition systems , 1994 .

[51]  Robert McNaughton,et al.  Infinite Games Played on Finite Graphs , 1993, Ann. Pure Appl. Logic.

[52]  Wolfgang Thomas,et al.  A Concatenation Game and the Dot-Depth Hierarchy , 1987, Computation Theory and Logic.

[53]  Amir Pnueli,et al.  The Glory of the Past , 1985, Logic of Programs.

[54]  Wolfgang Thomas,et al.  Logical Specifications of Infinite Computations , 1993, REX School/Symposium.

[55]  M. Rabin Automata on Infinite Objects and Church's Problem , 1972 .

[56]  J. Richard Büchi Regular canonical systems , 1964 .

[57]  C. Michaux,et al.  LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS , 1994 .

[58]  Damian Niwinski,et al.  Fixed points vs. infinite generation , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[59]  Andrzej Wlodzimierz Mostowski,et al.  Regular expressions for infinite trees and a standard form of automata , 1984, Symposium on Computation Theory.

[60]  Edmund M. Clarke,et al.  Verification Tools for Finite-State Concurrent Systems , 1993, REX School/Symposium.

[61]  Wolfgang Thomas,et al.  Regular Tree Languages Without Unary Symbols are Star-Free , 1993, FCT.

[62]  Robert McNaughton,et al.  Testing and Generating Infinite Sequences by a Finite Automaton , 1966, Inf. Control..

[63]  Igor Walukiewicz,et al.  Monadic Second Order Logic on Tree-Like Structures , 1996, STACS.

[64]  T. Henzinger The theory of hybrid automata , 1996, LICS 1996.

[65]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[66]  Wolfgang Thomas,et al.  NONDETERMINISM VERSUS DETERMINISM OF FINITE AUTOMATA OVER DIRECTED ACYCLIC GRAPHS , 1994 .

[67]  N. Klarlund Progress measures, immediate determinacy, and a subset construction for tree automata , 1992 .

[68]  Ludwig Staiger,et al.  Automatentheoretische und automatenfreie Charakterisierungen topologischer Klassen regulärer Folgenmengen , 1974, J. Inf. Process. Cybern..

[69]  R. McNaughton,et al.  Counter-Free Automata , 1971 .

[70]  Didier Caucal,et al.  On infinite transition graphs having a decidable monadic theory , 1996, Theor. Comput. Sci..

[71]  Bruno Courcelle,et al.  Monadic Second-Order Definable Graph Transductions: A Survey , 1994, Theor. Comput. Sci..

[72]  Joseph R. Shoenfield,et al.  Mathematical logic , 1967 .

[73]  Wolfgang Thomas An application of the Ehrenfeucht-Fraisse game in formal language theory , 1984 .

[74]  Dominique Perrin,et al.  Finite Automata , 1958, Philosophy.

[75]  David E. Muller,et al.  The Theory of Ends, Pushdown Automata, and Second-Order Logic , 1985, Theor. Comput. Sci..

[76]  Wolfgang Thomas On Logics, Tilings, and Automata , 1991, ICALP.

[77]  Robert S. Streett Propositional Dynamic Logic of looping and converse , 1981, STOC '81.

[78]  Danièle Beauquier,et al.  Factors of Words , 1989, ICALP.

[79]  Thomas Schwentick,et al.  Logics For Context-Free Languages , 1994, CSL.

[80]  E. Börger Computation Theory and Logic , 1987, Lecture Notes in Computer Science.

[81]  Madhavan Mukund,et al.  Determinizing Büchi Asnchronous Automata , 1995, FSTTCS.

[82]  Robert P. Kurshan,et al.  Computer-Aided Verification of Coordinating Processes: The Automata-Theoretic Approach , 2014 .

[83]  Wolfgang Thomas,et al.  On the Synthesis of Strategies in Infinite Games , 1995, STACS.

[84]  J. Richard Büchi,et al.  Using Determinancy of Games to Eliminate Quantifiers , 1977, FCT.

[85]  J. R. Büchi On a Decision Method in Restricted Second Order Arithmetic , 1990 .

[86]  Andrzej Ehrenfeucht,et al.  T-structures, T-functions, and texts , 1993, Theor. Comput. Sci..

[87]  Thomas Wilke,et al.  Computing the Wadge Degree, the Lifschitz Degree, and the Rabin Index of a Regular Language of Infinite Words in Polynomial Time , 1995, TAPSOFT.

[88]  Alasdair Urquhart,et al.  Temporal Logic , 1971 .

[89]  Kousha Etessami,et al.  An Until hierarchy for temporal logic , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[90]  Volker Diekert,et al.  The Book of Traces , 1995 .

[91]  Pierre Wolper,et al.  Reasoning About Infinite Computations , 1994, Inf. Comput..

[92]  Moshe Y. Vardi An Automata-Theoretic Approach to Linear Temporal Logic , 1996, Banff Higher Order Workshop.

[93]  Olivier Carton Chain Automata , 1994, Theor. Comput. Sci..

[94]  Giora Slutzki,et al.  Parallel and Two-Way Automata on Directed Ordered Acyclic Graphs , 1981, Inf. Control..

[95]  Andreas Podelski,et al.  Tree Automata and Languages , 1992 .

[96]  J. R. Büchi,et al.  Solving sequential conditions by finite-state strategies , 1969 .

[97]  Alex K. Simpson,et al.  Computational Adequacy in an Elementary Topos , 1998, CSL.

[98]  Imre Simon,et al.  Piecewise testable events , 1975, Automata Theory and Formal Languages.

[99]  Madhavan Mukund,et al.  Determinizing Asynchronous Automata , 1993 .

[100]  Andrzej Wlodzimierz Mostowski Hierarchies of Weak Automata and Weak Monadic Formulas , 1991, Theor. Comput. Sci..

[101]  Jörg Flum,et al.  Finite model theory , 1995, Perspectives in Mathematical Logic.

[102]  David E. Muller,et al.  Simulating Alternating Tree Automata by Nondeterministic Automata: New Results and New Proofs of the Theorems of Rabin, McNaughton and Safra , 1995, Theor. Comput. Sci..

[103]  Danièle Beauquier,et al.  Automata on Infinite Trees with Counting Constraints , 1993, TAPSOFT.

[104]  Wolfgang Thomas,et al.  Classifying Regular Events in Symbolic Logic , 1982, J. Comput. Syst. Sci..

[105]  Ronald Fagin,et al.  On Monadic NP vs. Monadic co-NP , 1995, Inf. Comput..

[106]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[107]  Igor Walukiewicz,et al.  Automata for the Modal mu-Calculus and related Results , 1995, MFCS.

[108]  R. Suzanne Zeitman,et al.  Unforgettable Forgetful Determinacy , 1994, J. Log. Comput..

[109]  Klaus W. Wagner,et al.  On omega-Regular Sets , 1979, Inf. Control..

[110]  Robert S. Streett,et al.  Propositional Dynamic Logic of Looping and Converse Is Elementarily Decidable , 1982, Inf. Control..

[111]  Jerzy Tiuryn,et al.  Logics of Programs , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[112]  S. Safra,et al.  On the complexity of omega -automata , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[113]  Thomas Wilke,et al.  Specifying Timed State Sequences in Powerful Decidable Logics and Timed Automata , 1994, FTRTFT.

[114]  John Doner,et al.  Tree Acceptors and Some of Their Applications , 1970, J. Comput. Syst. Sci..

[115]  Alexei L. Semenov,et al.  Decidability of Monadic Theories , 1984, MFCS.

[116]  E. Muller David,et al.  Alternating automata on infinite trees , 1987 .

[117]  Shmuel Safra,et al.  Exponential determinization for ω-automata with strong-fairness acceptance condition (extended abstract) , 1992, STOC '92.

[118]  Danièle Beauquier,et al.  Automata on Infinite Trees with Counting Constraints , 1995, Inf. Comput..

[119]  Francine Blanchet-Sadri,et al.  Some Logical Characterizations of the Dot-Depth Hierarchy and Applications , 1995, J. Comput. Syst. Sci..

[120]  Dominique Perrin,et al.  On the Expressive Power of Temporal Logic , 1993, J. Comput. Syst. Sci..

[121]  J. R. Büchi Regular Canonical Systems , 1964 .

[122]  Damian Niwinski,et al.  Fixed point characterization of weak monadic logic definable sets of trees , 1992, Tree Automata and Languages.

[123]  Colin Stirling,et al.  Modal and Temporal Logics for Processes , 1996, Banff Higher Order Workshop.

[124]  J. Büchi Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[125]  Kenneth L. McMillan,et al.  Symbolic model checking , 1992 .

[126]  Roger Villemaire,et al.  Presburger Arithmetic and Recognizability of Sets of Natural Numbers by Automata: New Proofs of Cobham's and Semenov's Theorems , 1996, Ann. Pure Appl. Log..

[127]  A. Prasad Sistla,et al.  On Model-Checking for Fragments of µ-Calculus , 1993, CAV.

[128]  Yves Métivier,et al.  Partial Commutation and Traces , 1997, Handbook of Formal Languages.

[129]  Sophie Tison,et al.  The theory of ground rewrite systems is decidable , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[130]  M. Rabin Decidability of second-order theories and automata on infinite trees , 1968 .

[131]  Raymond E. Miller,et al.  Varieties of Formal Languages , 1986 .

[132]  Calvin C. Elgot,et al.  Decidability and Undecidability of Extensions of Second (First) Order Theory of (Generalized) Successor , 1966, J. Symb. Log..

[133]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[134]  Thomas Wilke,et al.  Locally Threshold Testable Languages of Infinite Words , 1993, STACS.

[135]  Jim Alves-Foss,et al.  Higher Order Logic Theorem Proving and its Applications 8th International Workshop, Aspen Grove, Ut, Usa, September 11-14, 1995 : Proceedings , 1995 .

[136]  Detlef Seese,et al.  Interpretability and tree automata: A simple way to solve algorithmic problems on graphs closely related to trees , 1992, Tree Automata and Languages.

[137]  David A. Basin,et al.  Hardware Verification using Monadic Second-Order Logic , 1995, CAV.

[138]  L. Staiger Research in the theory of Ω-languages , 1987 .

[139]  Peter Øhrstrøm,et al.  Temporal Logic , 1994, Lecture Notes in Computer Science.

[140]  Anca Muscholl,et al.  Logical Definability on Infinite Traces , 1996, Theor. Comput. Sci..

[141]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.