On simultaneously determinizing and complementing omega -automata

The authors give a construction to determine and complement simultaneously a Buchi automaton in infinite strings, with an exponential blowup in states and a linear blowup in the number of pairs. An exponential lower bound is already known. The previous best construction was double exponential. The present result permits exponentially improved essentially optimal decision procedures for various modal logics of programs. It also gives exponentially improved conversions between various kinds of omega automata.<<ETX>>

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

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

[3]  Amir Pnueli,et al.  The temporal logic of programs , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[4]  Richard E. Ladner,et al.  Propositional Dynamic Logic of Regular Programs , 1979, J. Comput. Syst. Sci..

[5]  Vaughan R. Pratt,et al.  Process logic: preliminary report , 1979, POPL.

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

[7]  Dexter Kozen,et al.  RESULTS ON THE PROPOSITIONAL’p-CALCULUS , 2001 .

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

[9]  Rohit Parikh,et al.  Propositional game logic , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[10]  A. Prasad Sistla,et al.  Deciding Full Branching Time Logic , 1985, Inf. Control..

[11]  A. Prasad Sistla,et al.  Deciding branching time logic , 1984, STOC '84.

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

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

[14]  Moshe Y. Vardi.  The Taming of Converse: Reasoning about Two-way Computations , 1985, Logic of Programs.

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

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

[17]  E. Allen Emerson,et al.  The complexity of tree automata and logics of programs , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[18]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

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