An improved algorithm for determinization of weighted and fuzzy automata

For a given weighted finite automaton over a strong bimonoid we construct its reduced Nerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics. We show that the reduced Nerode automaton is even smaller than the Nerode automaton, which was previously used in determinization related to this semantics. We determine necessary and sufficient conditions under which the reduced Nerode automaton is finite and provide an efficient algorithm which computes the reduced Nerode automaton whenever it is finite. In determinization of weighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crisp-deterministic automata than any other known determinization algorithm.

[1]  Yongming Li,et al.  Finite Automata Based on Quantum Logic and Their Determinization , 2007, ArXiv.

[2]  G. Grätzer.  General Lattice Theory , 1978 .

[3]  Rob J. van Glabbeek,et al.  Five Determinisation Algorithms , 2008, CIAA.

[4]  Mehryar Mohri,et al.  Minimization algorithms for sequential transducers , 2000, Theor. Comput. Sci..

[5]  Benedikt Bollig.  Formal Models of Communicating Systems - Languages, Automata, and Monadic Second-Order Logic , 2006 .

[6]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[7]  James A. Anderson.  Automata theory with modern applications , 2006 .

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

[9]  Krishnendu Chatterjee,et al.  Quantitative Languages , 2008, CSL.

[10]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[11]  Mingsheng Ying,et al.  Automata Theory Based on Quantum Logic II , 2000 .

[12]  Arto Salomaa,et al.  Semirings, Automata, Languages , 1985, EATCS Monographs on Theoretical Computer Science.

[13]  QiuDaowen.  Automata theory based on quantum logic , 2007 .

[14]  Symeon Bozapalidis,et al.  Fuzzy tree language recognizability , 2010, Fuzzy Sets Syst..

[15]  Mehryar Mohri,et al.  Finite-State Transducers in Language and Speech Processing , 1997, CL.

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

[17]  Miroslav Ciric,et al.  Determinization of fuzzy automata with membership values in complete residuated lattices , 2008, Inf. Sci..

[18]  Daniel Kirsten,et al.  On the Determinization of Weighted Automata , 2005, J. Autom. Lang. Comb..

[19]  Symeon Bozapalidis,et al.  On the recognizability of fuzzy languages II , 2008, Fuzzy Sets Syst..

[20]  Christos G. Cassandras,et al.  Introduction to Discrete Event Systems , 1999, The Kluwer International Series on Discrete Event Dynamic Systems.

[21]  Manfred Droste,et al.  Determinization of weighted finite automata over strong bimonoids , 2010, Inf. Sci..

[22]  Symeon Bozapalidis,et al.  On the recognizability of Fuzzy languages I , 2006, Fuzzy Sets Syst..

[23]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[24]  Daowen Qiu,et al.  Automata theory based on quantum logic: some characterizations , 2004, Inf. Comput..

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

[26]  Miroslav Ciric,et al.  Formal power series and regular operations on fuzzy languages , 2010, Inf. Sci..

[27]  Thomas Lengauer,et al.  Unstructured Path Problems and the Making of Semirings (Preliminary Version) , 1991, WADS.

[28]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[29]  Mingsheng Ying,et al.  A theory of computation based on quantum logic (I) , 2004, 2005 IEEE International Conference on Granular Computing.

[30]  Manfred Droste,et al.  Weighted finite automata over strong bimonoids , 2010, Inf. Sci..

[31]  Krishnendu Chatterjee,et al.  Expressiveness and Closure Properties for Quantitative Languages , 2009, LICS.

[32]  Mingsheng Ying,et al.  Automata Theory Based on Quantum Logic. (I) , 2000 .

[33]  Daowen Qiu,et al.  Automata theory based on quantum logic: Reversibilities and pushdown automata , 2007, Theor. Comput. Sci..

[34]  Berndt Farwer,et al.  ω-automata , 2002 .

[35]  W. G. V. Hoorn,et al.  Fundamental notions in the theory of seminearrings , 1967 .

[36]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

[37]  Krishnendu Chatterjee,et al.  Alternating Weighted Automata , 2009, FCT.

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

[39]  Yongming Li,et al.  Finite automata based on quantum logic and monadic second-order quantum logic , 2010, Science in China Series F: Information Sciences.

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

[41]  Miroslav Ciric,et al.  Myhill-Nerode type theory for fuzzy languages and automata , 2010, Fuzzy Sets Syst..

[42]  Witold Pedrycz,et al.  Fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids , 2005, Fuzzy Sets Syst..

[43]  J. Mordeson,et al.  Fuzzy Automata and Languages: Theory and Applications , 2002 .

[44]  Radim Belohlávek,et al.  Determinism and fuzzy automata , 2002, Inf. Sci..

[45]  George J. Klir,et al.  Fuzzy sets and fuzzy logic , 1995 .

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

[47]  Raffaele Giancarlo,et al.  On the Determinization of Weighted Finite Automata , 2000, SIAM J. Comput..