Cycle detection in computation tree logic

Abstract We introduce Cycle- CTL ⋆ , an extension of CTL ⋆ with cycle quantifications that are able to predicate over cycles. The introduced logic turns out to be very expressive. Indeed, we prove that it strictly extends CTL ⋆ and is orthogonal to μ Calculus . We also give an evidence of its usefulness by providing few examples involving non-regular properties. We extensively investigate both the model-checking and satisfiability problems for Cycle- CTL ⋆ and some of its variants/fragments.

[1]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[2]  Saul A. Kripke,et al.  Semantical Considerations on Modal Logic , 2012 .

[3]  Joseph Y. Halpern,et al.  "Sometimes" and "not never" revisited: on branching versus linear time (preliminary report) , 1983, POPL '83.

[4]  Aniello Murano,et al.  Cycle Detection in Computation Tree Logic , 2016, GandALF.

[5]  Thomas Wilke,et al.  Automata logics, and infinite games: a guide to current research , 2002 .

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

[7]  Rajeev Alur,et al.  Deterministic generators and games for Ltl fragments , 2004, TOCL.

[8]  Aniello Murano,et al.  Pushdown module checking , 2010, Formal Methods Syst. Des..

[9]  Aniello Murano,et al.  Reasoning about Strategies: on the Satisfiability Problem , 2016, Log. Methods Comput. Sci..

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

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

[12]  Aniello Murano,et al.  Reasoning About Strategies: On the Model-Checking Problem , 2011, ArXiv.

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

[14]  Krishnendu Chatterjee,et al.  Finitary winning in ω-regular games , 2009, TOCL.

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

[16]  Aniello Murano,et al.  Typeness for omega-regular Automata , 2004, Int. J. Found. Comput. Sci..

[17]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 2002, JACM.

[18]  Wieslaw Zielonka,et al.  Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees , 1998, Theor. Comput. Sci..

[19]  Moshe Y. Vardi.  Reasoning about The Past with Two-Way Automata , 1998, ICALP.

[20]  Thomas A. Henzinger,et al.  Finitary fairness , 1998, TOPL.

[21]  Aniello Murano,et al.  Prompt Alternating-Time Epistemic Logics , 2016, KR.

[22]  E. Allen Emerson,et al.  The Complexity of Tree Automata and Logics of Programs , 1999, SIAM J. Comput..

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

[24]  Mimmo Parente,et al.  Enriched µ-Calculi Module Checking , 2007, Log. Methods Comput. Sci..

[25]  Orna Kupferman,et al.  From liveness to promptness , 2009, Formal Methods Syst. Des..

[26]  Aniello Murano,et al.  On Promptness in Parity Games , 2015, Fundam. Informaticae.

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

[28]  Amir Pnueli,et al.  Once and for all , 1995, J. Comput. Syst. Sci..