The Common Fragment of CTL and LTL

It is well-known thatCTL andLTL have incomparable expressive power. In this paper, we give an inductive definition of thoseACTL formulas that can be expressed in LTL . In addition, we obtain a procedure to decide whether an ACTL formula lies inLTL , and show that this problem isPSPACEcomplete. By omitting path quantifiers, we get an inductive definition of the LTL formulas expressible in ACTL . We can show that the fragment defined by our logic represents exactly those LTL formulas the negation of which can be represented by a 1-weak B üchi automaton and that for this fragment, the representing automaton can be chosen to be of size linear in the size of the formula.

[1]  Robert P. Kurshan,et al.  Computer-Aided Verification of Coordinating Processes: The Automata-Theoretic Approach , 2014 .

[2]  Moshe Y. Vardi.  On the complexity of modular model checking , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[3]  Orna Kupferman,et al.  Relating linear and branching model checking , 1998, PROCOMET.

[4]  Edmund M. Clarke,et al.  Expressibility results for linear-time and branching-time logics , 1988, REX Workshop.

[5]  Zohar Manna,et al.  Temporal Verification of Reactive Systems , 1995, Springer New York.

[6]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[7]  Robin Milner,et al.  An Algebraic Definition of Simulation Between Programs , 1971, IJCAI.

[8]  Edmund M. Clarke,et al.  Reasoning about networks with many identical finite-state processes , 1986, PODC '86.

[9]  Martin Peschke,et al.  Design and Validation of Computer Protocols , 2003 .

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

[11]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[12]  Pierre Wolper,et al.  Simple on-the-fly automatic verification of linear temporal logic , 1995, PSTV.

[13]  Edmund M. Clarke,et al.  Model checking, abstraction, and compositional verification , 1993 .

[14]  E. Emerson,et al.  Modalities for model checking (extended abstract): branching time strikes back , 1985, ACM-SIGACT Symposium on Principles of Programming Languages.

[15]  Orna Kupferman,et al.  Freedom, weakness, and determinism: from linear-time to branching-time , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[16]  Orna Kupferman,et al.  Module Checking , 1996, Inf. Comput..

[17]  Tiziano Villa,et al.  VIS: A System for Verification and Synthesis , 1996, CAV.

[18]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[19]  Kenneth L. McMillan,et al.  Symbolic model checking , 1992 .

[20]  Pierre Wolper,et al.  Reasoning About Infinite Computations , 1994, Inf. Comput..

[21]  Moshe Y. Vardi.  Linear vs. branching time: a complexity-theoretic perspective , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).