Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore.

[1]  Paul Gastin,et al.  Satisfiability and Model Checking for MSO-definable Temporal Logics are in PSPACE , 2003, CONCUR.

[2]  Paul Gastin,et al.  Uniform Satisfiability in PSPACE for Local Temporal Logics Over Mazurkiewicz Traces , 2007, Fundam. Informaticae.

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

[4]  Anca Muscholl,et al.  A Kleene theorem and model checking algorithms for existentially bounded communicating automata , 2006, Inf. Comput..

[5]  Benedikt Bollig,et al.  Message-passing automata are expressively equivalent to EMSO logic , 2006, Theor. Comput. Sci..

[6]  P. Madhusudan,et al.  Beyond Message Sequence Graphs , 2001, FSTTCS.

[7]  Daniel Brand,et al.  On Communicating Finite-State Machines , 1983, JACM.

[8]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching Time Temporal Logic , 2008, 25 Years of Model Checking.

[9]  J. Davenport.  Editor , 1960 .

[10]  Paul Gastin,et al.  Local temporal logic is expressively complete for cograph dependence alphabets , 2004, Inf. Comput..

[11]  Carsten Lutz,et al.  PDL with Intersection and Converse is 2EXP-complete , 2007, Algorithmic-Logical Theory of Infinite Structures.

[12]  Benedikt Bollig,et al.  Muller message-passing automata and logics , 2008, Inf. Comput..

[13]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[14]  Benedikt Bollig,et al.  Distributed Muller Automata and Logics , 2006 .

[15]  Wolfgang Thomas,et al.  The monadic quantifier alternation hierarchy over graphs is infinite , 1997, Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science.

[16]  Ramaswamy Ramanujam,et al.  Reasoning about Message Passing in Finite State Environments , 2000, ICALP.

[17]  Doron A. Peled,et al.  Specification and Verification of Message Sequence Charts , 2000, FORTE.

[18]  Benedikt Bollig,et al.  Propositional Dynamic Logic for Message-Passing Systems , 2007, FSTTCS.

[19]  P. S. Thiagarajan,et al.  A Product Version of Dynamic Linear Time Temporal Logic , 1997, CONCUR.

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

[21]  Paul Gastin,et al.  Uniform satisfiability problem for local temporal logics over Mazurkiewicz traces , 2010, Inf. Comput..

[22]  Moshe Y. Vardi.  Nontraditional Applications of Automata Theory , 1994, TACS.

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

[24]  Yaacov Choueka,et al.  Theories of Automata on omega-Tapes: A Simplified Approach , 1974, J. Comput. Syst. Sci..

[25]  Wolfgang Thomas,et al.  Automata on Infinite Objects , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[26]  Ramaswamy Ramanujam,et al.  Reasoning about layered message passing systems , 2004, Comput. Lang. Syst. Struct..

[27]  Wojciech Penczek,et al.  Model-checking of causality properties , 1995, Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science.

[28]  Anca Muscholl,et al.  Infinite-state high-level MSCs: Model-checking and realizability , 2002, J. Comput. Syst. Sci..

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

[30]  P. S. Thiagarajan,et al.  Dynamic Linear Time Temporal Logic , 1997, Ann. Pure Appl. Log..