Complementation of Finitely Ambiguous Büchi Automata

A nondeterministic automaton is finitely ambiguous if for each input there is at most finitely many accepting runs. We prove that the complement of the \(\omega \)-language accepted by a finitely ambiguous Buchi automaton with n states is accepted by an unambiguous Buchi automaton with \(2\times 5^n\) states.

[1]  Hing Leung.  Descriptional complexity of nfa of different ambiguity , 2005, Int. J. Found. Comput. Sci..

[2]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[3]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

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

[5]  Qiqi Yan.  Lower Bounds for Complementation of omega-Automata Via the Full Automata Technique , 2008, Log. Methods Comput. Sci..

[6]  Arto Salomaa,et al.  Ambiguity, Nondeterminism and State Complexity of Finite Automata , 2017, Acta Cybern..

[7]  Helmut Seidl,et al.  On the Degree of Ambiguity of Finite Automata , 1991, Theor. Comput. Sci..

[8]  Satoru Miyano,et al.  Alternating Finite Automata on omega-Words , 1984, CAAP.

[9]  Pierre Wolper,et al.  The Complementation Problem for Büchi Automata with Applications to Temporal Logic (Extended Abstract) , 1985, ICALP.

[10]  Jozef Jirásek,et al.  Operations on Unambiguous Finite Automata , 2016, DLT.

[11]  P.R.J. Asveld.  Review of "R.E. Stearns & H.B. Hunt III: On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata, SIAM J. Comput. 14 (1985) 598-611" , 1987 .

[12]  Thomas Colcombet.  Unambiguity in Automata Theory , 2015, DCFS.

[13]  Christof Löding,et al.  Efficient inclusion testing for simple classes of unambiguous ω-automata , 2012, Inf. Process. Lett..

[14]  Ernst L. Leiss,et al.  Succint Representation of Regular Languages by Boolean Automata , 1981, Theor. Comput. Sci..

[15]  Christel Baier,et al.  Markov Chains and Unambiguous Büchi Automata , 2016, CAV.

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

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

[18]  Harry B. Hunt,et al.  On the Equivalence and Containment Problems for Unambiguous Regular Expressions, Regular Grammars and Finite Automata , 1985, SIAM J. Comput..

[19]  Pierre Wolper,et al.  The Complementation Problem for Büchi Automata with Appplications to Temporal Logic , 1987, Theor. Comput. Sci..

[20]  Thomas Wilke,et al.  Complementation, Disambiguation, and Determinization of Büchi Automata Unified , 2008, ICALP.

[21]  André Arnold.  Rational omega-Languages are Non-Ambiguous , 1983, Theor. Comput. Sci..

[22]  Orna Kupferman,et al.  Büchi Complementation Made Tighter , 2006, Int. J. Found. Comput. Sci..