Results on Alternating-Time Temporal Logics with Linear Past

We investigate the succinctness gap between two known equally-expressive and different linearpast extensions of standard CTL∗ (resp., ATL∗). We establish by formal non-trivial arguments that the ‘memoryful’ linear-past extension (the history leading to the current state is taken into account) can be exponentially more succinct than the standard ‘local’ linear-past extension (the history leading to the current state is forgotten). As a second contribution, we consider the ATL-like fragment, denoted ATLlp, of the known ‘memoryful’ linear-past extension of ATL∗. We show that ATLlp is strictly more expressive than ATL, and interestingly, it can be exponentially more succinct than the more expressive logic ATL∗. Moreover, we prove that both satisfiability and model-checking for the logic ATLlp are Exptime-complete. Digital Object Identifier 10.4230/LIPIcs...

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

[2]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1999 .

[3]  Igor Walukiewicz,et al.  Automata for the Modal mu-Calculus and related Results , 1995, MFCS.

[4]  Moshe Y. Vardi.  A temporal fixpoint calculus , 1988, POPL '88.

[5]  François Laroussinie,et al.  Specification in CTL+Past for Verification in CTL , 1999, Inf. Comput..

[6]  Dov M. Gabbay,et al.  The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems , 1987, Temporal Logic in Specification.

[7]  Bernd Finkbeiner,et al.  Satisfiability and Finite Model Property for the Alternating-Time mu-Calculus , 2006, CSL.

[8]  Aniello Murano,et al.  Relentful strategic reasoning in alternating-time temporal logic , 2010, J. Log. Comput..

[9]  Nicolas Markey,et al.  ATL with Strategy Contexts and Bounded Memory , 2009, LFCS.

[10]  Sven Schewe.  ATL* Satisfiability Is 2EXPTIME-Complete , 2008, ICALP.

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

[12]  Wolfgang Thomas,et al.  Computation Tree Logic CTL* and Path Quantifiers in the Monadic Theory of the Binary Tree , 1987, ICALP.

[13]  Philippe Schnoebelen,et al.  A Hierarchy of Temporal Logics with Past , 1995, Theor. Comput. Sci..

[14]  Christel Baier,et al.  Principles of model checking , 2008 .

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

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

[17]  Constantin Enea,et al.  An alternating-time temporal logic with knowledge, perfect recall and past: axiomatisation and model-checking , 2011, J. Appl. Non Class. Logics.

[18]  Wojciech Jamroga,et al.  Module Checking of Strategic Ability , 2015, AAMAS.

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

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

[21]  Wojciech Jamroga,et al.  Agents with truly perfect recall in alternating-time temporal logic , 2014, AAMAS.

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

[23]  Orna Kupferman,et al.  Weak alternating automata and tree automata emptiness , 1998, STOC '98.

[24]  Wojciech Jamroga,et al.  Alternating-time temporal logics with irrevocable strategies , 2007, TARK '07.

[25]  Laura Bozzelli.  The Complexity of CTL* + Linear Past , 2008, FoSSaCS.

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

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

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

[29]  Aniello Murano,et al.  On the Complexity of ATL and ATL* Module Checking , 2017, GandALF.