Oracle Circuits for Branching-Time Model Checking

A special class of oracle circuits with tree-vector form is introduced. It is shown that they can be evaluated in deterministic polynomial-time with a polylog number of adaptive queries to an NP oracle. This framework allows us to evaluate the precise computational complexity of model checking for some branching-time logics where it was known that the problem is NP-hard and coNP-hard.

[1]  Philippe Schnoebelen,et al.  The Complexity of Propositional Linear Temporal Logics in Simple Cases , 1998, Inf. Comput..

[2]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[3]  Klaus W. Wagner,et al.  Bounded Query Classes , 1990, SIAM J. Comput..

[4]  Thomas Wilke,et al.  Timed Alternating Tree Automata: The Automata-Theoretic Solution to the TCTL Model Checking Problem , 1999, ICALP.

[5]  Klaus W. Wagner,et al.  More Complicated Questions About Maxima and Minima, and Some Closures of NP , 1986, Theor. Comput. Sci..

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

[7]  Philippe Schnoebelen,et al.  The Complexity of Temporal Logic Model Checking , 2002, Advances in Modal Logic.

[8]  Alexander Moshe Rabinovich,et al.  An Infinite Hierarchy of Temporal Logics over Branching Time , 2002, Inf. Comput..

[9]  Carlos Seara,et al.  Complexity Classes Between ThetaPk and DeltaPk , 1996, RAIRO Theor. Informatics Appl..

[10]  Samuel R. Buss,et al.  On Truth-Table Reducibility to SAT , 1991, Inf. Comput..

[11]  Klaus W. Wagner.  More Complicated Questions About Maxima and Minima, and Some Closures of NP , 1987, Theor. Comput. Sci..

[12]  Philippe Schnoebelen,et al.  On Model Checking Durational Kripke Structures , 2002, FoSSaCS.

[13]  Philippe Schnoebelen,et al.  Temporal logic with forgettable past , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[14]  Wa Halang,et al.  REAL-TIME SYSTEMS .2. , 1989 .

[15]  Stephan Merz,et al.  Model Checking , 2000 .

[16]  Georg Gottlob.  NP trees and Carnap's modal logic , 1995, JACM.

[17]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[18]  Ron Koymans,et al.  Specifying real-time properties with metric temporal logic , 1990, Real-Time Systems.

[19]  Pierre Wolper,et al.  An automata-theoretic approach to branching-time model checking , 2000, JACM.

[20]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[21]  Alexander Moshe Rabinovich,et al.  Expressive Power of Temporal Logics , 2002, CONCUR.

[22]  Joseph Y. Halpern,et al.  Decision procedures and expressiveness in the temporal logic of branching time , 1982, STOC '82.

[23]  Chin-Laung Lei,et al.  Modalities for Model Checking: Branching Time Logic Strikes Back , 1987, Sci. Comput. Program..

[24]  Philippe Schnoebelen,et al.  Model Checking CTL+ and FCTL is Hard , 2001, FoSSaCS.

[25]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[26]  Christos H. Papadimitriou,et al.  Two remarks on the power of counting , 1983, Theoretical Computer Science.