Bounded model-checking of discrete duration calculus

Fraenzle and Hansen investigated the model-checking problem of the subset of Duration Calculus without individual variables and quantifications w.r.t. some approximation semantics by reduction to the decision problem of Presburger Arithmetic, thus obtained a model-checking algorithm with 4-fold exponential complexity [6,7]. As an alternative, inspired by their work, we consider the bounded model-checking problem of the subset in the context of the standard discrete-time semantics in this paper. Based on our previous work [20], we reduce this problem to the reachability problem of timed automata. The complexity of our approach is singly exponential in the size of formulas and quadratic in the number of states of models. We implement our approach using UPPAAL and demonstrate its efficiency by some examples.

[1]  Víctor A. Braberman,et al.  On checking timed automata for linear duration invariants , 1998, Proceedings 19th IEEE Real-Time Systems Symposium (Cat. No.98CB36279).

[2]  Miaomiao Zhang,et al.  Model Checking Linear Duration Invariants of Networks of Automata , 2009, FSEN.

[3]  Zhou Chaochen,et al.  Duration Calculus: A Formal Approach to Real-Time Systems , 2004 .

[4]  P. Pandya.  Specifying and Deciding Quantified Discrete-time Duration Calculus Formulae using DCVALID , 2000 .

[5]  Supratik Chakraborty,et al.  Bounded Validity Checking of Interval Duration Logic , 2005, TACAS.

[6]  Martin Fränzle,et al.  Efficient Model Checking for Duration Calculus Based on Branching-Time Approximations , 2008, 2008 Sixth IEEE International Conference on Software Engineering and Formal Methods.

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

[8]  Chaochen Zhou.  Linear Duration Invariants , 1994, FTRTFT.

[9]  C. A. R. Hoare,et al.  A Calculus of Durations , 1991, Inf. Process. Lett..

[10]  Michael R. Hansen,et al.  Duration Calculus: A Formal Approach to Real-Time Systems (Monographs in Theoretical Computer Science. an Eatcs Seris) , 2004 .

[11]  Valentin Goranko,et al.  A Road Map of Interval Temporal Logics and Duration Calculi , 2004, J. Appl. Non Class. Logics.

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

[13]  Ben C. Moszkowski,et al.  A Temporal Logic for Multilevel Reasoning about Hardware , 1985, Computer.

[14]  Michael R. Hansen,et al.  Model-checking discrete duration calculus , 1994, Formal Aspects of Computing.

[15]  Xuandong Li,et al.  Checking Linear Duration Invariants by Linear Programming , 1996, ASIAN.

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

[17]  Michael R. Hansen,et al.  On Tool Support for Duration Calculus on the Basis of Presburger Arithmetic , 2011, 2011 Eighteenth International Symposium on Temporal Representation and Reasoning.

[18]  Kim G. Larsen,et al.  A Tutorial on Uppaal , 2004, SFM.

[19]  Dang Van Hung,et al.  Verifying Linear Duration Constraints of Timed Automata , 2004, ICTAC.

[20]  Martin Fränzle,et al.  Efficient Model Checking for Duration Calculus? , 2009, Int. J. Softw. Informatics.

[21]  Viet Nam,et al.  Verification of linear duration invariants by model checking CTL properties , 2008 .

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

[23]  Roland Meyer,et al.  Model Checking Duration Calculus: A Practical Approach , 2006, ICTAC.

[24]  Naijun Zhan,et al.  On hierarchically developing reactive systems , 2010, Inf. Comput..