Characteristic formulae for timed automata

This paper offers characteristic formula constructions in the real-time logic L v for several behavioural relations between (states of) timed automata. The behavioural relations studied in this work are timed (bi)similarity, timed ready simulation, faster-than bisimilarity and timed trace inclusion. The characteristic formulae delivered by our constructions have size which is linear in that of the timed automaton they logically describe. This also applies to the characteristic formula for timed bisimulation equivalence, for which an exponential space construction was previously offered by Laroussinie, Larsen and Weise.

[1]  Bernhard Steffen,et al.  Characteristic Formulae for Processes with Divergence , 1994, Inf. Comput..

[2]  Robert M. Keller,et al.  Formal verification of parallel programs , 1976, CACM.

[3]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum I , 2001, Handbook of Process Algebra.

[4]  Rance Cleaveland,et al.  A linear-time model-checking algorithm for the alternation-free modal mu-calculus , 1993, Formal Methods Syst. Des..

[5]  Glynn Winskel,et al.  Language, Semantics, and Methods for Cryptographic Protocols , 2000 .

[6]  Rance Cleaveland,et al.  A linear-time model-checking algorithm for the alternation-free modal mu-calculus , 1993, Formal Methods Syst. Des..

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

[8]  Joost Engelfriet,et al.  Determinacy - (Observation Equivalence = Trace Equivalence) , 1985, Theor. Comput. Sci..

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

[10]  Luca Aceto,et al.  2-Nested Simulation Is Not Finitely Equationally Axiomatizable , 2000, STACS.

[11]  Luca Aceto,et al.  Is your model checker on time? On the complexity of model checking for timed modal logics , 1999, J. Log. Algebraic Methods Program..

[12]  Kim Guldstrand Larsen,et al.  From Timed Automata to Logic - and Back , 1995 .

[13]  Joseph Sifakis,et al.  A Modal Characterization of Observational Congruence on Finite Terms of CCS , 1986, Inf. Control..

[14]  Thomas Hune,et al.  Modeling a Language for Embedded Systems in Timed Automata , 2000 .

[15]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[16]  Philippe Schnoebelen,et al.  The State Explosion Problem from Trace to Bisimulation Equivalence , 2000, FoSSaCS.

[17]  Dexter Kozen,et al.  RESULTS ON THE PROPOSITIONAL’p-CALCULUS , 2001 .

[18]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[19]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[20]  Rance Cleaveland,et al.  Computing Behavioural Relations, Logically , 1991, ICALP.

[21]  Luca Aceto,et al.  Characteristic Formulae for Timed Automata , 2000 .

[22]  Rob J. van Glabbeek,et al.  The Linear Time-Branching Time Spectrum (Extended Abstract) , 1990, CONCUR.

[23]  Vinodchandran Variyam.  A Note on NP \ coNP=poly , 2000 .

[24]  Rajeev Alur,et al.  Heuristics for Hierarchical Partitioning with Application to Model Checking , 2000, CHARME.

[25]  Anders B. Sandholm,et al.  Using Automata in Control Synthesis. A Case Study , 2000 .

[26]  Jirí Srba.  Complexity of Weak Bisimilarity and Regularity for BPA and BPP , 2000, EXPRESS.

[27]  Olivier Danvy,et al.  Syntactic accidents in program analysis: on the impact of the CPS transformation , 2000, ICFP '00.

[28]  Faron Moller,et al.  Relating Processes With Respect to Speed , 1991, CONCUR.

[29]  Wang Yi,et al.  Real-Time Behaviour of Asynchronous Agents , 1990, CONCUR.

[30]  R. J. vanGlabbeek.  The linear time - branching time spectrum , 1990 .

[31]  Kim G. Larsen,et al.  CMC: A Tool for Compositional Model-Checking of Real-Time Systems , 1998, FORTE.

[32]  Luca Aceto,et al.  Is Your Model Checker on Time? On the Complexity of Model Checking for Timed Modal Logics , 1999 .

[33]  Albert R. Meyer,et al.  Bisimulation can't be traced , 1988, POPL '88.

[34]  Kim G. Larsen,et al.  Bisimulation through Probabilistic Testing , 1991, Inf. Comput..

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

[36]  Edmund M. Clarke,et al.  Characterizing Finite Kripke Structures in Propositional Temporal Logic , 1988, Theor. Comput. Sci..

[37]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.