Action Planning for Directed Model Checking of Petri Nets

Petri nets are fundamental to the analysis of distributed systems especially infinite-state systems. Finding a particular marking corresponding to a property violation in Petri nets can be reduced to exploring a state space induced by the set of reachable markings. Typical exploration(reachability analysis) approaches are undirected and do not take into account any knowledge about the structure of the Petri net. This paper proposes heuristic search for enhanced exploration to accelerate the search. For different needs in the system development process, we distinguish between different sorts of estimates. Treating the firing of a transition as an action applied to a set of predicates induced by the Petri net structure and markings, the reachability analysis can be reduced to finding a plan to an AI planning problem. Having such a reduction broadens the horizons for the application of AI heuristic search planning technology. In this paper we discuss the transformations schemes to encode Petri nets into PDDL. We show a concise encoding of general place-transition nets in Level 2 PDDL2.2, and a specification for bounded place-transition nets in ADL/STRIPS. Initial experiments with an existing planner are presented.

[1]  B. E. Eckbo,et al.  Appendix , 1826, Epilepsy Research.

[2]  李幼升,et al.  Ph , 1989 .

[3]  Marco Roveri,et al.  Recent Advances in AI Planning , 1999, Lecture Notes in Computer Science.

[4]  Stefan Edelkamp,et al.  Promela Planning , 2003, SPIN.

[5]  Paolo Traverso,et al.  Automatic OBDD-Based Generation of Universal Plans in Non-Deterministic Domains , 1998, AAAI/IAAI.

[6]  Fausto Giunchiglia,et al.  Planning via Model Checking: A Decision Procedure for AR , 1997, ECP.

[7]  Marco Pistore,et al.  Planning as Model Checking for Extended Goals in Non-deterministic Domains , 2001, IJCAI.

[8]  James C. Corbett,et al.  Evaluating Deadlock Detection Methods for Concurrent Software , 1996, IEEE Trans. Software Eng..

[9]  Gérard Berthelot,et al.  Transformations and Decompositions of Nets , 1986, Advances in Petri Nets.

[10]  Blai Bonet,et al.  Planning as heuristic search , 2001, Artif. Intell..

[11]  S. Edelkamp,et al.  Abstraction Databases in Theory and Model Checking Practice , 2004 .

[12]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[13]  Stefan Edelkamp,et al.  Cost-Algebraic Heuristic Search , 2005, AAAI.

[14]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[15]  Bernhard Nebel,et al.  The FF Planning System: Fast Plan Generation Through Heuristic Search , 2011, J. Artif. Intell. Res..

[16]  Edwin P. D. Pednault,et al.  ADL: Exploring the Middle Ground Between STRIPS and the Situation Calculus , 1989, KR.

[17]  Stephan Melzer,et al.  Deadlock Checking Using Net Unfoldings , 1997, CAV.

[18]  Gérard Berthelot,et al.  Checking properties of nets using transformation , 1985, Applications and Theory in Petri Nets.

[19]  S. Edelkamp,et al.  Engineering Benchmarks for Planning: the Domains Used in the Deterministic Part of IPC-4 , 2006, J. Artif. Intell. Res..

[20]  Fahiem Bacchus,et al.  Using temporal logics to express search control knowledge for planning , 2000, Artif. Intell..

[21]  Stefan Edelkamp,et al.  Abstraction in directed model checking , 2004 .

[22]  Maria Fox,et al.  PDDL2.1: An Extension to PDDL for Expressing Temporal Planning Domains , 2003, J. Artif. Intell. Res..

[23]  Gerard J. Holzmann,et al.  The SPIN Model Checker - primer and reference manual , 2003 .

[24]  Stefan Edelkamp,et al.  Taming Numbers and Durations in the Model Checking Integrated Planning System , 2003, PuK.

[25]  Stefan Edelkamp,et al.  Generalizing the Relaxed Planning Heuristic to Non-linear Tasks , 2004, KI.

[26]  C. Petri.  Kommunikation mit Automaten , 1962 .

[27]  Patrik Haslum,et al.  Extending TALplanner with Concurrency and Resources , 2000, ECAI.

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

[29]  Stefan Edelkamp,et al.  Action Planning for Graph Transition Systems , 2005 .

[30]  Michel Barbeau,et al.  Planning Control Rules for Reactive Agents , 1997, Artif. Intell..

[31]  Jörg Hoffmann,et al.  The Metric-FF Planning System: Translating ''Ignoring Delete Lists'' to Numeric State Variables , 2003, J. Artif. Intell. Res..

[32]  Stefan Edelkamp,et al.  Directed explicit-state model checking in the validation of communication protocols , 2004, International Journal on Software Tools for Technology Transfer.

[33]  Patrick Fabiani,et al.  Planning with tokens: an approach between satisfaction and optimisation , 2000, PuK.

[34]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[35]  Ilkka Niemelä,et al.  Answer Set Programming and Bounded Model Checking , 2001, Answer Set Programming.

[36]  Larry S. Davis,et al.  Pattern Databases , 1979, Data Base Design Techniques II.

[37]  Stefan Edelkamp,et al.  Towards Realistic Benchmarks for Planning: the Domains Used in the Classical Part of IPC-4 , 2004 .