Model Checking Duration Calculus: A Practical Approach

Model checking of real-time systems with respect to Duration Calculus (DC) specifications requires the translation of DC formulae into automata-based semantics. This task is difficult to automate. The existing algorithms provide a limited DC coverage and do not support compositional verification. We propose a translation algorithm that advances the applicability of model checking tools to real world applications. Our algorithm significantly extends the subset of DC that can be handled. It decomposes DC specifications into sub-properties that can be verified independently. The decomposition bases on a novel distributive law for DC. We implemented the algorithm as part of our tool chain for the automated verification of systems comprising data, communication, and real-time aspects. Our translation facilitated a successful application of the tool chain on an industrial case study from the European Train Control System (ETCS).

[1]  Kenneth L. McMillan,et al.  Interpolation and SAT-Based Model Checking , 2003, CAV.

[2]  Paritosh K. Pandya,et al.  Interval Duration Logic: Expressiveness and Decidability , 2002, Theory and Practice of Timed Systems @ ETAPS.

[3]  Henning Dierks,et al.  Constructing Test Automata from Graphical Real-Time Requirements , 2002, FTRTFT.

[4]  Graeme Smith,et al.  The Object-Z Specification Language , 1999, Advances in Formal Methods.

[5]  Jochen Hoenicke,et al.  Combining Specification Techniques for Processes, Data and Time , 1998, ZUM.

[6]  Andrew William Roscoe,et al.  The Theory and Practice of Concurrency , 1997 .

[7]  Andreas Podelski,et al.  ARMC: The Logical Choice for Software Model Checking with Abstraction Refinement , 2007, PADL.

[8]  Andreas Podelski,et al.  A Model Checker based on Abstraction Refinement , 2002 .

[9]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[10]  Martin Fränzle,et al.  Deciding an Interval Logic with Accumulated Durations , 2007, TACAS.

[11]  Holger Hermanns,et al.  From StoCharts to MoDeST: a comparative reliability analysis of train radio communications , 2005, WOSP '05.

[12]  Andreas Podelski,et al.  Transition predicate abstraction and fair termination , 2005, POPL '05.

[13]  Hassen Saïdi,et al.  Construction of Abstract State Graphs with PVS , 1997, CAV.

[14]  Günter Hommel,et al.  Towards modeling and evaluation of ETCS real-time communication and operation , 2005, Journal of Systems and Software.

[15]  Ingo Brückner,et al.  Slicing Concurrent Real-Time System Specifications for Verification , 2007, IFM.

[16]  Viorica Sofronie-Stokkermans,et al.  Constraint solving for interpolation , 2007, J. Symb. Comput..

[17]  Johannes Faber,et al.  Verifying CSP-OZ-DC Specifications with Complex Data Types and Timing Parameters , 2007, IFM.

[18]  Shankara Narayanan Krishna,et al.  Modal Strength Reduction in Quantified Discrete Duration Calculus , 2005, FSTTCS.

[19]  Kim Guldstrand Larsen,et al.  The power of reachability testing for timed automata , 2003, Theor. Comput. Sci..

[20]  Ahmed Bouajjani,et al.  From Duration Calculus To Linear Hybrid Automata , 1995, CAV.

[21]  Edmund M. Clarke,et al.  Counterexample-Guided Abstraction Refinement , 2000, CAV.

[22]  Jochen Hoenicke,et al.  Model-Checking of Specifications Integrating Processes, Data and Time , 2005, FM.

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

[24]  Moshe Y. Vardi Verification of Concurrent Programs: The Automata-Theoretic Framework , 1991, Ann. Pure Appl. Log..

[25]  Andreas Podelski,et al.  Abstraction Refinement for Termination , 2005, SAS.

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

[27]  Martin Fränzle,et al.  Model-checking dense-time Duration Calculus , 2004, Formal Aspects of Computing.

[28]  Thomas A. Henzinger,et al.  HYTECH: A Model Checker for Hybrid Systems , 1997, CAV.

[29]  Jochen Hoenicke,et al.  CSP-OZ-DC: A Combination of Specification Techniques for Processes, Data and Time , 2002, Nord. J. Comput..

[30]  Michael R. Hansen,et al.  Decidability and Undecidability Results for Duration Calculus , 1993, STACS.