skip to main content
research-article

Action Synthesis for Branching Time Logic: Theory and Applications

Authors Info & Claims
Published:09 September 2015Publication History
Skip Abstract Section

Abstract

The article introduces a parametric extension of Action-Restricted Computation Tree Logic called pmARCTL. A symbolic fixed-point algorithm providing a solution to the exhaustive parameter synthesis problem is proposed. The parametric approach allows for an in-depth system analysis and synthesis of the correct parameter values. The time complexity of the problem and the algorithm is provided. An existential fragment of pmARCTL (pmEARCTL) is identified, in which all of the solutions can be generated from a minimal and unique base. A method for computing this base using symbolic methods is provided. The prototype tool SPATULA implementing the algorithm is applied to the analysis of three benchmarks: faulty Train-Gate-Controller, Peterson’s mutual exclusion protocol, and a generic pipeline processing network. The experimental results show efficiency and scalability of our approach compared to the naive solution to the problem.

References

  1. R. Alur, K. Etessami, S. La Torre, and D. Peled. 2001. Parametric temporal logic for “model measuring.” ACM Transactions on Computational Logic 2, 3, 388--407. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. R. Alur, T. Henzinger, and M. Vardi. 1993. Parametric real-time reasoning. In Proceedings of the 25th Annual Symposium on Theory of Computing. ACM, New York, NY, 592--601. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. É. André, L. Fribourg, U. Kühne, and R. Soulat. 2012. IMITATOR 2.5: A tool for analyzing robustness in scheduling problems. In FM 2012: Formal Methods. Lecture Notes in Computer Science, Vol. 7436. Springer, 33--36.Google ScholarGoogle Scholar
  4. C. Baier and J.-P. Katoen. 2008. Principles of Model Checking. MIT Press, Cambridge, MA. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. F. Belardinelli, A. V. Jones, and A. Lomuscio. 2011. Model checking temporal-epistemic logic using alternating tree automata. Fundamenta Informaticae: Concurrency Specification and Programming 112, 1, 19--37. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. V. Bruyére, E. Dall’Olio, and J. Raskin. 2008. Durations and parametric model-checking in timed automata. ACM Transactions on Computational Logic 9, 2, 1--23. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. E. Clarke and E. A. Emerson. 1981. Design and synthesis of synchronization skeletons for branching-time temporal logic. In Logics of Programs. Lecture Notes in Computer Science, Vol. 131. Springer, 52--71. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. A. Classen, P. Heymans, P.-Y. Schobbens, and A. Legay. 2011. Symbolic model checking of software product lines. In Proceedings of the 33rd International Conference on Software Engineering (ICSE’11). ACM, New York, NY, 321--330. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. O. Coudert, J. C. Madre, H. Fraisse, and H. Touati. 1993. Implicit prime cover computation: An overview. In Proceedings of the Synthesis and Simulation Meeting and International Interchange (SASIMI’93).Google ScholarGoogle Scholar
  10. C. Daskalakis, R. M. Karp, E. Mossel, S. Riesenfeld, and E. Verbin. 2011. Sorting and selection in posets. SIAM Journal on Computing 40, 3, 597--622. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. B. Di Giampaolo, S. La Torre, and M. Napoli. 2010. Parametric metric interval temporal logic. In Language and Automata Theory and Applications. Lecture Notes in Computer Science, Vol. 6031. Springer, 249--260. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. J. Goldsmith, M. Hagen, and M. Mundhenk. 2008. Complexity of DNF minimization and isomorphism testing for monotone formulas. Information and Computation 206, 6, 760--775. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. T. Hune, J. Romijn, M. Stoelinga, and F. Vaandrager. 2002. Linear parametric model checking of timed automata. Journal of Logic and Algebraic Programming 52--53, 183--220.Google ScholarGoogle ScholarCross RefCross Ref
  14. A. V. Jones, M. Knapik, A. Lomuscio, and W. Penczek. 2012. Group synthesis for parametric temporal-epistemic logic. In Proceedings of the 11th International Conference on Autonomous Agents and Multi-Agent Systems (AAMAS’12). 1107--1114. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. G. Katz and D. Peled. 2010. Code mutation in verification and automatic code correction. In Tools and Algorithms for the Construction and Analysis of Systems. Lecture Notes in Computer Science, Vol. 6015. Springer, 435--450. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. M. Knapik. 2014. SPATULA, Simple Parametric Verification Tool. Retrieved August 10, 2015, from https://michalknapik.github.io/spatula.Google ScholarGoogle Scholar
  17. M. Knapik, A. Męski, and W. Penczek. 2014. Action synthesis for branching time logic: Theory and applications. In Proceedings of the 14th International Conference on Application of Concurrency to System Design (ACSD’14). IEEE, Los Alamitos, CA, 1--10. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. C. Pecheur and F. Raimondi. 2006. Symbolic model checking of logics with actions. In Model Checking and Artificial Intelligence. Lecture Notes in Computer Science, Vol. 4428. Springer, 113--128. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. D. Peled. 1993. All from one, one for all: On model checking using representatives. In Computer Aided Verification. Lecture Notes in Computer Science, Vol. 697. Springer, 409--423. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. G. L. Peterson. 1981. Myths about the mutual exclusion problem. Information Processing Letters 12, 3, 115--116.Google ScholarGoogle ScholarCross RefCross Ref
  21. W. Quine. 1952. The problem of simplifying truth functions. American Mathematical Monthly 59, 8, 521--531.Google ScholarGoogle ScholarCross RefCross Ref
  22. P. Schnoebelen. 2002. The complexity of temporal logic model checking. In Advances in Modal Logic, Vol. 4. World Scientific Publishing, 393--436.Google ScholarGoogle Scholar
  23. F. Somenzi. 2012. CUDD: CU Decision Diagram Package. Retrieved August 10, 2015, from http://vlsi.colorado.edu/∼fabio/CUDD/cuddIntro.html.Google ScholarGoogle Scholar

Index Terms

  1. Action Synthesis for Branching Time Logic: Theory and Applications

            Recommendations

            Comments

            Login options

            Check if you have access through your login credentials or your institution to get full access on this article.

            Sign in

            Full Access

            PDF Format

            View or Download as a PDF file.

            PDF

            eReader

            View online with eReader.

            eReader
            About Cookies On This Site

            We use cookies to ensure that we give you the best experience on our website.

            Learn more

            Got it!