The Complementation Problem for Büchi Automata with Applications to Temporal Logic (Extended Abstract)

The problem of complementing Buchi automata arises when developing procedures for temporal logics of programs. Unfortunately, previously known constructions for complementing Buchi automata involve a doubly exponential blow-up in the size of the automaton. We present a construction that involves only an exponential blow-up. We use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic.

[1]  Yaacov Choueka,et al.  Theories of Automata on omega-Tapes: A Simplified Approach , 1974, J. Comput. Syst. Sci..

[2]  Pierre Wolper,et al.  Reasoning about infinite computation paths , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[3]  Samuel Eilenberg,et al.  Automata, languages, and machines. A , 1974, Pure and applied mathematics.

[4]  Pierre Wolper,et al.  Yet Another Process Logic (Preliminary Version) , 1983, Logic of Programs.

[5]  J. Richard Büchi,et al.  The monadic second order theory of ω1 , 1973 .

[6]  S. Shelah,et al.  The monadic theory of ω 2 , 1983 .

[7]  Aravinda Prasad Sistla,et al.  Theoretical issues in the design and verification of distributed systems , 1983 .

[8]  Larry J. Stockmeyer,et al.  Improved upper and lower bounds for modal logics of programs , 1985, STOC '85.

[9]  D. Siefkes.  Büchi's monadic second order successor arithmetic , 1970 .

[10]  Edward L. Robertson.  Structure of complexity in the weak monadic second-order theories of the natural numbers , 1974, STOC '74.

[11]  Pierre Wolper.  Temporal Logic Can Be More Expressive , 1983, Inf. Control..

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

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

[14]  H. Alaiwan,et al.  Equivalence of Infinite Behavior of Finite Automata , 1984, Theor. Comput. Sci..

[15]  Pierre Wolper,et al.  Automata theoretic techniques for modal logics of programs: (Extended abstract) , 1984, STOC '84.

[16]  Albert R. Meyer,et al.  WEAK MONADIC SECOND ORDER THEORY OF SUCCESSOR IS NOT ELEMENTARY-RECURSIVE , 1973 .

[17]  Boris A. Trakhtenbrot,et al.  Finite automata : behavior and synthesis , 1973 .

[18]  David Harel,et al.  Process logic: Expressiveness, decidability, completeness , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[19]  Amir Pnueli.  The Temporal Semantics of Concurrent Programs , 1981, Theor. Comput. Sci..

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

[21]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[22]  Pierre Wolper,et al.  Automata theoretic techniques for modal logics of programs: (Extended abstract) , 1984, STOC '84.

[23]  A. Prasad Sistla,et al.  The complexity of propositional linear temporal logics , 1982, STOC '82.

[24]  Pierre Wolper,et al.  Synthesis of Communicating Processes from Temporal Logic Specifications , 1981, TOPL.

[25]  Albert R. Meyer,et al.  The Equivalence Problem for Regular Expressions with Squaring Requires Exponential Space , 1972, SWAT.