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Updatable timed automata with one updatable clock

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Abstract

Updatable timed automata (UTAs) proposed by Bouyer et.al., is an extension of timed automata (TAs) having the extra ability to update clocks in a more elaborate way than simply reset them to zero. The reachability of UTAs is generally undecidable, which can be easily gained by regarding a pair of clocks as updatable counters. This paper investigates a subclass of UTAs by restricting the number of updatable clocks to be one. We will show that (1) the reachability of general UTAs with one updatable clock (UTA1s) is still undecidable, and (2) that of UTA1s under diagonal-free constraints is decidable, and the complexity is Pspace-complete. The former is achieved by encoding Minsky machines to the general UTA1s, where two counters are simulated by the updatable clock. The latter is gained by regarding a region of a UTA1 to be an unbounded digiword, and encoding sets of digiwords that are accepted by a one counter automaton where regions are generated as the value of the counter.

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References

  1. Alur R, Dill D L. A theory of timed automata. Theor Comput Sci, 1994, 126: 183–235

    Article  MathSciNet  MATH  Google Scholar 

  2. Bouyer P, Dufourd C, Fleury E, et al. Are timed automata updatable? In: Proceedings of the 12th International Conference on Computer Aided Verification, Chicago, 2000. 464–479

    Chapter  Google Scholar 

  3. Bouyer P, Dufourd C, Fleury E, et al. Expressiveness of updatable timed automata. In: Proceedings of International Symposium on Mathematical Foundations of Computer, Bratislava, 2000. 232–242

    Google Scholar 

  4. Bouyer P, Dufourd C, Fleury E, et al. Updatable timed automata. Theor Comput Sci, 2004, 321: 291–345

    Article  MathSciNet  MATH  Google Scholar 

  5. Minsky M L. Computation: Finite and Infinite Machines. Upper Saddle River: Prentice-Hall, 1967

    Google Scholar 

  6. Bouyer P. Forward analysis of updatable timed automata. Form Method Syst Des, 2004, 24: 281–320

    Article  MATH  Google Scholar 

  7. Fang B B, Li G Q, Fang L, et al. A refined algorithm for reachability analysis of updatable timed automata. In: Proceedings of IEEE International Conference on the Software Quality, Reliability and Security - Companion, Vancouver, 2015. 230–236

    Google Scholar 

  8. Henzinger T A, Kopke P W, Puri A, et al. What’s decidable about hybrid automata? J Comput Syst Sci, 1998, 57: 94–124

    Article  MathSciNet  MATH  Google Scholar 

  9. Wen Y Q, Li G Q, Yuen S. On reachability analysis of updatable timed automata with one updatable clock. In: Proceedings of International Workshop on Structured Object-Oriented Formal Language and Method, Pairs, 2015, 147–161

    Google Scholar 

  10. Abdulla P A, Atig M F, Stenman J. Dense-timed pushdown automata. In: Proceedings of 27th Annual IEEE Symposium on Logic in Computer Science, Dubrovnik, 2012. 35–44

    Google Scholar 

  11. Li G Q, Ogawa M, Yuen S. Nested timed automata with frozen clocks. In: Proceedings of International Conference on Formal Modeling and Analysis of Timed Systems, Madrid, 2015, 189–205

    Chapter  Google Scholar 

  12. Jancar P, Kucera A, Moller F, et al. DP lower bounds for equivalence-checking and model-checking of one-counter automata. Inform Comput, 2004, 188: 1–19

    Article  MathSciNet  MATH  Google Scholar 

  13. Haase C, Kreutzer S, Ouaknine J, et al. Reachability in succinct and parametric one-counter automata. In: Proceedings of the International Conference on Concurrency Theory, Bologna, 2009. 369–383

    Google Scholar 

  14. Schwoon S. Model-checking pushdown system. Dissertation for Ph.D. Degree. Munich: Technical University of Munich, 2000

    Google Scholar 

  15. Demri S, Gascon R. The effects of bounding syntactic resources on presburger LTL. J Logic Comput, 2009, 19: 1541–1575

    Article  MathSciNet  MATH  Google Scholar 

  16. Fersman E, Krcal P, Pettersson P, et al. Task automata: schedulability, decidability and undecidability. Inform Comput, 2007, 205: 1149–1172

    Article  MathSciNet  MATH  Google Scholar 

  17. Ouaknine J, Worrell J. On the language inclusion problem for timed automata: closing a decidability gap. In: Proceedings of the 19th IEEE Symposium on Logic in Computer Science, Turku, 2004. 54–63

    Google Scholar 

  18. Abdulla P A, Jonsson B. Verifying networks of timed processes. In: Proceedings of International Conference on Tools and Algorithms for the Construction and Analysis of Systems, Lisbon, 1998. 298–312

    Chapter  Google Scholar 

  19. Abdulla P A, Jonsson B. Model checking of systems with many identical time processes. Theor Comput Sci, 2003, 290: 241–264

    Article  MATH  Google Scholar 

  20. Li G Q, Cai X J, Ogawa M, et al. Nested timed automata. In: Proceedings of International Conference on Formal Modeling and Analysis of Timed Systems, Buenos Aires, 2013. 168–182

    Chapter  Google Scholar 

  21. Choffrut C, Goldwurm M. Timed automata with periodic clock constraints. J Autom Lang Comb, 2000, 5: 371–404

    MathSciNet  MATH  Google Scholar 

  22. Demichelis F, Zielonka W. Controlled timed automata. In: Proceedings of the 9th International Conference on Concurrency Theory, Nice, 1998. 455–469

    Google Scholar 

  23. Bouchy F, Finkel A, Sangnier A. Reachability in timed counter systems. Electr Notes Theor Comput Sci, 2009, 239: 167–178

    Article  MathSciNet  MATH  Google Scholar 

  24. Alur R, La Torre S, Pappas G J. Optimal paths in weighted timed automata. In: Proceedings of International Workshop on Hybrid Systems: Computation and Control, Rome, 2001, 49–62

    Chapter  Google Scholar 

  25. Behrmann G, Fehnker A, Hune T, et al. Minimum-cost reachability for priced timed automata. In: Proceedings of the International Workshop on Hybrid Systems: Computation and Control, Rome, 2001, 147–161

    Chapter  Google Scholar 

  26. Bouyer P, Chevalier F. On conciseness of extensions of timed automata. J Autom Lang Combin 2005, 10: 393–405

    MathSciNet  MATH  Google Scholar 

  27. Suman P V, Pandya P K, Krishna S N, et al. Timed automata with integer resets: language inclusion and expressiveness. In: Proceedings of International Conference on Formal Modeling and Analysis of Timed Systems, Saint Malo, 2008. 78–92

    Chapter  Google Scholar 

  28. Suman P V, Pandya P K. Determinization and expressiveness of integer reset timed automata with silent transitions. In: Proceedings of International Conference on Language and Automata Theory and Applications, Tarragona, 2009, 728–739

    Chapter  Google Scholar 

  29. Trivedi A, Wojtczak D. Recursive timed automata. In: Proceedings of International Symposium on Automated Technology for Verification and Analysis, Singapore, 2010. 306–324

    Chapter  Google Scholar 

  30. Wen Y Q, Li G Q, Yuen S J. An over-approximation forward analysis for nested timed automata. In: Proceedings of International Workshop on Structured Object-Oriented Formal Language and Method, Luxembourg, 2014. 62–80

    Google Scholar 

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Acknowledgments

This work was supported by NSFC-JSPS Bilateral Joint Research Project (Grant No. 61511140100), and National Natural Science Foundation of China (Grant Nos. 61472240, 61602224, 91318301).

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Authors and Affiliations

  1. BASICS, School of Software, Shanghai Jiao Tong University, Shanghai, 200240, China

    Guoqiang Li & Yunqing Wen

  2. Graduate School of Information Science, Nagoya University, Nagoya, 464-8601, Japan

    Shoji Yuen

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  1. Guoqiang Li
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  2. Yunqing Wen
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  3. Shoji Yuen
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Correspondence to Guoqiang Li.

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Li, G., Wen, Y. & Yuen, S. Updatable timed automata with one updatable clock. Sci. China Inf. Sci. 61, 012102 (2017). https://doi.org/10.1007/s11432-016-9027-y

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  • DOI: https://doi.org/10.1007/s11432-016-9027-y

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