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Preserving Partial-Order Runs in Parametric Time Petri Nets

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Published:19 December 2016Publication History
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Abstract

Parameter synthesis for timed systems aims at deriving parameter valuations satisfying a given property. In this article, we target concurrent systems. We use partial-order semantics for parametric time Petri nets as a way to both cope with the well-known state-space explosion due to concurrency and significantly enhance the result of an existing synthesis algorithm. Given a reference parameter valuation, our approach synthesizes other valuations preserving the partial-order executions of the reference parameter valuation. We show the applicability of our approach using a tool applied to asynchronous circuits.

References

  1. Rajeev Alur and David L. Dill. 1994. A theory of timed automata. Theoretical Computer Science 126, 2, 183--235. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Rajeev Alur, Thomas A. Henzinger, and Moshe Y. Vardi. 1993. Parametric real-time reasoning. In Proceedings of the 25th Annual ACM Symposium on Theory of Computing (STOC’93). ACM, New York, NY, 592--601. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Étienne André, Thomas Chatain, Emmanuelle Encrenaz, and Laurent Fribourg. 2009. An inverse method for parametric timed automata. International Journal of Foundations of Computer Science 20, 5, 819--836. Google ScholarGoogle ScholarCross RefCross Ref
  4. Étienne André, Laurent Fribourg, Ulrich Kühne, and Romain Soulat. 2012. IMITATOR 2.5: A tool for analyzing robustness in scheduling problems. In FM 2010: Formal Methods. Lecture Notes in Computer Science, Vol. 7436. Springer, 33--36. Google ScholarGoogle ScholarCross RefCross Ref
  5. Étienne André and Nicolas Markey. 2015. Language preservation problems in parametric timed automata. In Formal Modeling and Analysis of Timed Systems. Lecture Notes in Computer Science, Vol. 9268. Springer, 27--43. Google ScholarGoogle ScholarCross RefCross Ref
  6. Étienne André, Laure Petrucci, and Giuseppe Pellegrino. 2013. Precise robustness analysis of time Petri nets with inhibitor arcs. In Formal Modeling and Analysis of Timed Systems. Lecture Notes in Computer Science, Vol. 8053. Springer, 1--15. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Étienne André and Romain Soulat. 2011. Synthesis of timing parameters satisfying safety properties. In Reachability Problems. Lecture Notes in Computer Science, Vol. 6945. Springer, 31--44. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Tuomas Aura and Johan Lilius. 2000. A causal semantics for time Petri nets. Theoretical Computer Science 243, 1--2, 409--447. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Roberto Bagnara, Patricia M. Hill, and Enea Zaffanella. 2008. The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Science of Computer Programming 72, 1--2, 3--21. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Johan Bengtsson, Bengt Jonsson, Johan Lilius, and Wang Yi. 1998. Partial order reductions for timed systems. In CONCUR ’98: Concurrency Theory. Lecture Notes in Computer Science, Vol. 1466. Springer, 485--500. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Béatrice Bérard, Franck Cassez, Serge Haddad, Didier Lime, and Olivier H. Roux. 2005. Comparison of the expressiveness of timed automata and time Petri nets. In Formal Modeling and Analysis of Timed Systems. Lecture Notes in Computer Science, Vol. 3829. Springer, 211--225. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Patricia Bouyer, Serge Haddad, and Pierre-Alain Reynier. 2006. Timed unfoldings for networks of timed automata. In Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, Vol. 4218. Springer, 292--306. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Laura Bozzelli and Salvatore La Torre. 2009. Decision problems for lower/upper bound parametric timed automata. Formal Methods in System Design 35, 2, 121--151. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Véronique Bruyère and Jean-François Raskin. 2007. Real-time model-checking: Parameters everywhere. Logical Methods in Computer Science 3, 1, 7.Google ScholarGoogle ScholarCross RefCross Ref
  15. Franck Cassez, Thomas Chatain, and Claude Jard. 2006. Symbolic unfoldings for networks of timed automata. In Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, Vol. 4218. Springer, 307--321. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Thomas Chatain and Claude Jard. 2006. Complete finite prefixes of symbolic unfoldings of safe time Petri nets. In Petri Nets and Other Models of Concurrency—ICATPN 2006. Lecture Notes in Computer Science, Vol. 4024. 125--145. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Rémy Chevallier, Emmanuelle Encrenaz-Tiphène, Laurent Fribourg, and Weiwen Xu. 2009. Timed verification of the generic architecture of a memory circuit using parametric timed automata. Formal Methods in System Design 34, 1, 59--81. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Robert Clarisó and Jordi Cortadella. 2005. Verification of concurrent systems with parametric delays using octahedra. In Proceedings of the 5th International Conference on Application of Concurrency to System Design (ACSD’05). IEEE, Los Alamitos, CA, 122--131. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Joost Engelfriet. 1991. Branching processes of Petri nets. Acta Informatica 28, 6, 575--591. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Thomas Hune, Judi Romijn, Mariëlle Stoelinga, and Frits W. Vaandrager. 2002. Linear parametric model checking of timed automata. Journal of Logic and Algebraic Programming 52-53, 183--220. Google ScholarGoogle ScholarCross RefCross Ref
  21. Aleksandra Jovanović, Didier Lime, and Olivier H. Roux. 2015. Integer parameter synthesis for timed automata. IEEE Transactions on Software Engineering 41, 5, 445--461. Google ScholarGoogle ScholarCross RefCross Ref
  22. Victor Khomenko. 2012. Punf. Retrieved November 27, 2016, from http://homepages.cs.ncl.ac.uk/victor.khomenko/tools/punf/.Google ScholarGoogle Scholar
  23. Micha Knapik and Wojciech Penczek. 2012. Bounded model checking for parametric timed automata. Transactions on Petri Nets and Other Models of Concurrency 5, 141--159. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Kim G. Larsen, Paul Pettersson, and Wang Yi. 1997. UPPAAL in a nutshell. International Journal on Software Tools for Technology Transfer 1, 1--2, 134--152. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Didier Lime, Olivier H. Roux, Charlotte Seidner, and Louis-Marie Traonouez. 2009. Romeo: A parametric model-checker for Petri nets with stopwatches. In Tools and Algorithms for the Construction and Analysis of Systems. Lecture Notes in Computer Science, Vol. 5505. Springer, 54--57. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Denis Lugiez, Peter Niebert, and Sarah Zennou. 2005. A partial order semantics approach to the clock explosion problem of timed automata. Theoretical Computer Science 345, 1, 27--59. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Nicolas Markey. 2011. Robustness in real-time systems. In Proceedings of the 6th International Symposium on Industrial Embedded Systems (SIES’11). IEEE, Los Alamitos, CA, 28--34. Google ScholarGoogle ScholarCross RefCross Ref
  28. Eric Mercer, Chris J. Myers, and Tomohiro Yoneda. 2002. Modular synthesis of timed circuits using partial order reduction. Electronic Notes in Theoretical Computer Science 65, 6, 180--201. Google ScholarGoogle ScholarCross RefCross Ref
  29. Philip M. Merlin and David J. Farber. 1976. Recoverability of communication protocols—implications of a theoretical study. IEEE Transactions on Communications, 9, 1036--1043. Google ScholarGoogle ScholarCross RefCross Ref
  30. Marius Minea. 1999. Partial order reduction for model checking of timed automata. In CONCUR ’99: Concurrency Theory. Lecture Notes in Computer Science, Vol. 1664. Springer, 431--446. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Marvin L. Minsky. 1967. Computation: Finite and Infinite Machines. Prentice Hall, Upper Saddle River, NJ. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Peter Niebert and Hongyang Qu. 2006. Adding invariants to event zone automata. In Formal Modeling and Analysis of Timed Systems. Lecture Notes in Computer Science, Vol. 4202. Springer, 290--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Wojciech Penczek and Agata Pólrola. 2001. Abstractions and partial order reductions for checking branching properties of time Petri nets. In Applications and Theory of Petri Nets. Lecture Notes in Computer Science, Vol. 2075. Springer, 323--342. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Florent Peres, Bernard Berthomieu, and François Vernadat. 2011. On the composition of time Petri nets. Discrete Event Dynamic Systems 21, 3, 395--424. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. César Rodríguez, Marcelo Sousa, Subodh Sharma, and Daniel Kroening. 2015. Unfolding-based partial order reduction. In Proceedings of the 26th Conference on Concurrency Theory (CONCUR’15). 456--469.Google ScholarGoogle Scholar
  36. Csar Rodrí and Stefan Schwoon. 2013. Cunf: A tool for unfolding and verifying Petri nets with read arcs. In Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, Vol. 8172. Springer, 492--495. Google ScholarGoogle ScholarCross RefCross Ref
  37. Alexander Schrijver. 1986. Theory of Linear and Integer Programming. John Wiley 8 Sons, New York, NY. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Stefan Schwoon. 2014. Mole—A Petri Net Unfolder. Retrieved November 27, 2016, from http://lsv.ens-cachan.fr/ schwoon/tools/mole/.Google ScholarGoogle Scholar
  39. Jun Sun, Yang Liu, Jin Song Dong, and Jun Pang. 2009. PAT: Towards flexible verification under fairness. In Computer Aided Verification. Lecture Notes in Computer Science, Vol. 5643. Springer, 709--714. Google ScholarGoogle ScholarDigital LibraryDigital Library
  40. Louis-Marie Traonouez, Bartosz Grabiec, Claude Jard, Didier Lime, and Olivier H. Roux. 2010. Symbolic unfolding of parametric stopwatch Petri nets. In Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, Vol. 6252. Springer, 291--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Louis-Marie Traonouez, Didier Lime, and Olivier H. Roux. 2009. Parametric model-checking of stopwatch Petri nets. Journal of Universal Computer Science 15, 17, 3273--3304.Google ScholarGoogle Scholar
  42. Irina Virbitskaite and E. Pokozy. 1999. A partial order method for the verification of time Petri nets. In Fundamentals of Computation Theory. Lecture Notes in Computer Science, Vol. 1684. Springer, 547--558. Google ScholarGoogle ScholarDigital LibraryDigital Library
  43. Tomohiro Yoneda and Bernd-Holger Schlingloff. 1997. Efficient verification of parallel real-time systems. Formal Methods in System Design 11, 2, 187--215. Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Hao Zheng, Eric Mercer, and Chris J. Myers. 2001. Automatic abstraction for verification of timed circuits and systems. In Computer Aided Verification. Lecture Notes in Computer Science, Vol. 2102. Springer, 182--193. Google ScholarGoogle ScholarDigital LibraryDigital Library

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