Weighted automata

Weighted automata are classical finite automata in which the transitions carry weights. 7 These weights may model quantitative properties like the amount of resources needed for executing 8 a transition or the probability or reliability of its successful execution. Using weighted automata, 9 we may also count the number of successful paths labeled by a given word. 10 As an introduction into this field, we present selected classical and recent results concentrating 11 on the expressive power of weighted automata. 12 2 M. Droste, D. Kuske

[1]  Kim G. Larsen,et al.  Optimal infinite scheduling for multi-priced timed automata , 2008, Formal Methods Syst. Des..

[2]  Manfred Droste,et al.  Weighted Automata and Regular Expressions over Valuation Monoids , 2011, Int. J. Found. Comput. Sci..

[3]  W. Marsden.  I and J , 2012 .

[4]  Mariëlle Stoelinga,et al.  An Introduction to Probabilistic Automata , 2002, Bull. EATCS.

[5]  Arto Salomaa,et al.  Automata-Theoretic Aspects of Formal Power Series , 1978, Texts and Monographs in Computer Science.

[6]  Manfred Droste,et al.  The Chomsky-SCHüTzenberger Theorem for Quantitative Context-Free Languages , 2012, Int. J. Found. Comput. Sci..

[7]  Rafael Peñaloza,et al.  Automata-Based Axiom Pinpointing , 2010, Journal of Automated Reasoning.

[8]  Manfred Droste,et al.  Weighted automata and multi-valued logics over arbitrary bounded lattices , 2012, Theor. Comput. Sci..

[9]  Petr Hájek,et al.  Metamathematics of Fuzzy Logic , 1998, Trends in Logic.

[10]  Orna Kupferman,et al.  What's Decidable about Weighted Automata? , 2011, ATVA.

[11]  I. Petre,et al.  Algebraic Systems and Pushdown Automata , 2009 .

[12]  M. Minsky.  Recursive Unsolvability of Post's Problem of "Tag" and other Topics in Theory of Turing Machines , 1961 .

[13]  Paul Gastin,et al.  On Aperiodic and Star-Free Formal Power Series in Partially Commuting Variables , 2007, Theory of Computing Systems.

[14]  Manfred Droste,et al.  Weighted automata and weighted logics with discounting , 2007, Theor. Comput. Sci..

[15]  Editors , 1986, Brain Research Bulletin.

[16]  Zoltán Ésik,et al.  A Unifying Kleene Theorem for Weighted Finite Automata , 2011, Rainbow of Computer Science.

[17]  Tero Harju,et al.  The Equivalence Problem of Multitape Finite Automata , 1991, Theor. Comput. Sci..

[18]  Kim G. Larsen,et al.  Infinite Runs in Weighted Timed Automata with Energy Constraints , 2008, FORMATS.

[19]  M. Droste,et al.  Semirings and Formal Power Series , 2009 .

[20]  Patrice Godefroid,et al.  Model Checking with Multi-valued Logics , 2004, ICALP.

[21]  John W. Woods,et al.  Digital Image Compression , 2012 .

[22]  Benedikt Bollig,et al.  Weighted versus Probabilistic Logics , 2009, Developments in Language Theory.

[23]  Manfred Droste,et al.  Weighted automata and weighted MSO logics for average and long-time behaviors , 2012, Inf. Comput..

[24]  Alois Panholzer,et al.  Gröbner Bases and the Defining Polynomial of a Context-Free Grammar Generating Function , 2005, J. Autom. Lang. Comb..

[25]  Helmut Seidl.  Finite Tree Automata with Cost Functions , 1992, CAAP.

[26]  Daniel Kirsten,et al.  Distance desert automata and the star height problem , 2005, RAIRO Theor. Informatics Appl..

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

[28]  Paulien ten Pas,et al.  Monadic second-order definable text languages , 1997, Theory of Computing Systems.

[29]  Ina Mäurer.  Weighted picture automata and weighted logics , 2006 .

[30]  J. Golan.  Semirings and their applications , 1999 .

[31]  Johan Schalkwyk,et al.  OpenFst: A General and Efficient Weighted Finite-State Transducer Library , 2007, CIAA.

[32]  Maurice Nivat,et al.  Transduction des langages de Chomsky , 1968 .

[33]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[34]  Christian Mathissen.  Definable transductions and weighted logics for texts , 2010, Theor. Comput. Sci..

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

[36]  Marsha Chechik,et al.  Model-checking infinite state-space systems with fine-grained abstractions using SPIN , 2001, SPIN '01.

[37]  Ina Fichtner.  Weighted Picture Automata and Weighted Logics , 2009, Theory of Computing Systems.

[38]  George Rahonis,et al.  Weighted Muller Tree Automata and Weighted Logics , 2007, J. Autom. Lang. Comb..

[39]  R. Alur,et al.  Adding nesting structure to words , 2006, JACM.

[40]  Symeon Bozapalidis,et al.  Representable Tree Series , 1994, Fundam. Informaticae.

[41]  Krishnendu Chatterjee,et al.  Quantitative languages , 2008, TOCL.

[42]  Kim G. Larsen,et al.  Minimum-Cost Reachability for Priced Timed Automata , 2001, HSCC.

[43]  Daniel Kirsten.  An Algebraic Characterization of Semirings for Which the Support of Every Recognizable Series Is Recognizable , 2009, MFCS.

[44]  Kosaburo Hashiguchi,et al.  Improved Limitedness Theorems on Finite Automata with Distance Functions , 1990, Theor. Comput. Sci..

[45]  Manfred Droste,et al.  A Kleene-Schützenberger theorem for weighted timed automata , 2008, Theor. Comput. Sci..

[46]  Mehryar Mohri,et al.  Weighted Automata Algorithms , 2009 .

[47]  Manfred Droste,et al.  Weighted finite automata over hemirings , 2013, Theor. Comput. Sci..

[48]  Jean Berstel,et al.  Recognizable Formal Power Series on Trees , 1982, Theor. Comput. Sci..

[49]  Dietrich Kuske.  Schützenberger's theorem on formal power series follows from Kleene's theorem , 2008, Theor. Comput. Sci..

[50]  L. Staiger.  Languages , 1997, Practice and Procedure of the International Criminal Tribunal for the Former Yugoslavia.

[51]  Nissim Francez,et al.  Finite-Memory Automata , 1994, Theor. Comput. Sci..

[52]  Daniel Kirsten.  The Support of a Recognizable Series over a Zero-Sum Free, Commutative Semiring Is Recognizable , 2009, Developments in Language Theory.

[53]  Christel Baier,et al.  Probabilistic ω-automata , 2012, JACM.

[54]  Antonio Restivo,et al.  On Cancellation Properties of Languages which are Supports of Ration Power Series , 1984, J. Comput. Syst. Sci..

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

[56]  W. Wechler.  The concept of fuzziness in automata and language theory , 1978 .

[57]  Zoltán Ésik,et al.  A Semiring-Semimodule Generalization of ω-Regular Languages II , 2005, J. Autom. Lang. Comb..

[58]  Kevin Knight,et al.  Tiburon: A Weighted Tree Automata Toolkit , 2006, CIAA.

[59]  Jean Berstel,et al.  Rational series and their languages , 1988, EATCS monographs on theoretical computer science.

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

[61]  Ingmar Meinecke.  Valuations of Weighted Automata: Doing It in a Rational Way , 2011, Algebraic Foundations in Computer Science.

[62]  Symeon Bozapalidis.  Effective construction of the syntactic algebra of a recognizable series on trees , 2005, Acta Informatica.

[63]  H. Vogler,et al.  Weighted Tree Automata and Tree Transducers , 2009 .

[64]  Jacques Sakarovitch,et al.  Elements of Automata Theory , 2009 .

[65]  Werner Kuich,et al.  Semirings and Formal Power Series: Their Relevance to Formal Languages and Automata , 1997, Handbook of Formal Languages.

[66]  Christian Mathissen,et al.  Weighted Logics for Nested Words and Algebraic Formal Power Series , 2008, ICALP.

[67]  Jarkko Kari.  Image Processing Using Finite Automata , 2006, Recent Advances in Formal Languages and Applications.

[68]  Manfred Droste,et al.  A Nivat Theorem for Weighted Timed Automata and Weighted Relative Distance Logic , 2014, ICALP.

[69]  Andreas Maletti,et al.  Survey: Weighted Extended Top-down Tree Transducers Part II - Application in Machine Translation , 2011, Fundam. Informaticae.

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

[71]  Werner Kuich.  Tree Transducers and Formal Tree Series , 1999, Acta Cybern..

[72]  Manfred Droste,et al.  Kleene and Büchi Theorems for Weighted Automata and Multi-valued Logics over Arbitrary Bounded Lattices , 2010, Developments in Language Theory.

[73]  Wojciech Zielonka,et al.  The Book of Traces , 1995 .

[74]  Kevin Knight,et al.  Applications of Weighted Automata in Natural Language Processing , 2009 .

[75]  Eleni Mandrali,et al.  Recognizable Tree Series with Discounting , 2009, Acta Cybern..

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

[77]  Daniel Krob,et al.  The Equality Problem for Rational Series with Multiplicities in the tropical Semiring is Undecidable , 1992, Int. J. Algebra Comput..

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

[79]  Eduardo D. Sontag.  On Some Questions of Rationality and Decidability , 1975, J. Comput. Syst. Sci..

[80]  S. Gottwald.  A Treatise on Many-Valued Logics , 2001 .

[81]  Wolfgang Thomas,et al.  Elements of an automata theory over partial orders , 1997, Partial Order Methods in Verification.

[82]  Anil Nerode,et al.  Automata theory and its applications , 2001 .

[83]  Johannes Waldmann.  Automatic Termination , 2009, RTA.

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

[85]  Manfred Droste,et al.  Weighted Automata and Weighted Logics with Discounting , 2007, CIAA.

[86]  J. Sakarovitch.  Rational and Recognisable Power Series , 2009 .

[87]  Karel Culik,et al.  Finite Automata Computing Real Functions , 1994, SIAM J. Comput..

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

[89]  Benedikt Bollig,et al.  Pebble Weighted Automata and Weighted Logics , 2014, TOCL.

[90]  M. Droste,et al.  Handbook of Weighted Automata , 2009 .

[91]  Karin Quaas.  MSO logics for weighted timed automata , 2011, Formal Methods Syst. Des..

[92]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[93]  Orna Kupferman,et al.  Lattice Automata , 2007, VMCAI.

[94]  Jean Berstel,et al.  Transductions and context-free languages , 1979, Teubner Studienbücher : Informatik.

[95]  Manfred Droste,et al.  Weighted Logics for Unranked Tree Automata , 2009, Theory of Computing Systems.

[96]  George J. Pappas,et al.  Optimal Paths in Weighted Timed Automata , 2001, HSCC.

[97]  Manfred Droste,et al.  Weighted Automata and Logics for Infinite Nested Words , 2014, LATA.

[98]  Jarkko Kari,et al.  Image compression using weighted finite automata , 1993, Comput. Graph..

[99]  Manfred Droste,et al.  Skew and infinitary formal power series , 2003, Theor. Comput. Sci..

[100]  Marcel Paul Schützenberger,et al.  On the Definition of a Family of Automata , 1961, Inf. Control..

[101]  Rais Gatic Bukharaev.  Theorie der stochastischen Automaten , 1995, Leitfäden der Informatik.

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

[103]  Krishnendu Chatterjee,et al.  Expressiveness and Closure Properties for Quantitative Languages , 2009, 2009 24th Annual IEEE Symposium on Logic In Computer Science.

[104]  Ina Fichtner,et al.  Traces, Series-Parallel Posets, and Pictures: A Weighted Study , 2009 .