Jie An
ABSTRACT
Extended Linear Duration Invariants (ELDI), an important subset of Duration Calculus, extends well-studied Linear Duration Invariants with logical connectives and the chop modality. It is known that the model checking problem of ELDI is undecidable with both the standard continuous-time and discrete-time semantics [12, 13], but it turns out to be decidable if only bounded execution fragments of timed automata are concerned in the context of the discrete-time semantics [36]. In this paper, we prove that this problem is still decidable in the continuous-time semantics, although it is well-known that model-checking Duration Calculus with the continuous-time semantics is much more complicated than the one with the discrete-time semantics. This is achieved by reduction to the validity of Quantified Linear Real Arithmetic (QLRA). Some examples are provided to illustrate the efficiency of our approach.
- R. Alur and D. L. Dill. 1994. A theory of timed automata. TCS 126(2) (1994), 183--235. Google Scholar
Digital Library
- J. Bengtsson and Y. Wang. 2004. Timed Automata: Semantics, Algorithms and Tools. In Lectures on Concurrency and Petri Nets: Advances in Petri Nets. 87--124.Google Scholar
- V. A. Braberman and D. V. Huang. 1998. On checking timed automata for linear duration invariants. In RTSS 1998. 264 - 273. Google ScholarDigital Library
- C. W. Brown. 2003. QEPCAD B: A program for computing with semialgebraic sets using CADs. ACM SIGSAM Bulletin 37, 4 (2003), 97--108. Google ScholarDigital Library
- G. Collins. 1975. Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. In 2nd GI Conference on Automata Theory and Formal Languages. 134--183. Google ScholarDigital Library
- W. Damm, M. Horbach, and V. Sofronie-Stokkermans. 2015. Decidability of Verification of Safety Properties of Spatial Families of Linear Hybrid Automata. In FroCoS 2015. 186--202. Google ScholarDigital Library
- W. Damm, C. Ihlemann, and V. Sofronie-Stokkermans. 2011. Decidability and complexity for the verification of safety properties of reasonable linear hybrid automata. In HSCC 2011. 73--82. Google ScholarDigital Library
- A. Dolzmann, A. Seidl, and T. Sturm. 2006. Redlog User Manual (Edition 3.1, for Redlog Version 3.06 (Reduce 3.8) ed.).Google Scholar
- A. Dolzmann, T. Sturm, and V. Weispfenning. 1998. A new approach for automatic theorem proving in real geometry. J. of Automated Reasoning 21, 3 (1998), 357--380. Google ScholarDigital Library
- M. Fränzle. 2004. Model-checking dense-time Duration Calculus. Formal Aspects of Computing 16, 2 (2004), 121--139. Google ScholarCross Ref
- M. Fränzle and M. R. Hansen. 2007. Deciding an interval logic with accumulated durations. In TACAS 2007. 201--215. Google ScholarDigital Library
- M. Fränzle and M. R. Hansen. 2008. Efficient model checking for Duration Calculus based on branching-time approximations. In SEFM 2008. 63--72. Google ScholarDigital Library
- M. Fränzle and M. R. Hansen. 2009. Efficient model checking for duration calculus. International Journal of Software and Informatics 3, 2-3 (2009), 171--196.Google Scholar
- V. Goranko, A. Montanari, and G. Sciavicco. 2004. A road map of interval temporal logics and duration calculi. J. of Applied Non-Classical Logics 14, 1-2 (2004), 9--54.Google ScholarCross Ref
- J. Y. Halpern, Z. Manna, and B. C. Moszkowski. 1983. A hardware semantics based on temporal intervals. In ICALP 1983. 278--291. Google ScholarDigital Library
- M. R. Hansen. 1994. Model-checking discrete Duration Calculus. Formal Aspects of Computing 6, 1 (1994), 826--845. Google ScholarCross Ref
- T. A. Henzinger. 1996. The theory of hybrid automata. In LICS 1996. 278--292. Google ScholarDigital Library
- C. Zhou. C. A. R. Hoare and A. P. Ravn. 1991. A calculus of durations. Inf. Proc. Let. 40, 5 (1991), 269--276.Google ScholarCross Ref
- K. G. Larsen, P. Pettersson, and Y. Wang. 1997. Uppaal in a nutshell. STTT 1, 1 (1997), 134--152.Google ScholarDigital Library
- X. Li. and D. V. Huang. 1996. Checking linear duration invariants by linear programming. In ASIAN 1996. 321--332. Google ScholarDigital Library
- X. Li, D. V. Huang, and T. Zheng. 1997. Checking hybrid automata for linear duration invariants. In ASIAN 1997. 166--180. Google ScholarDigital Library
- J. Liu. 2000. Real-Time Systems. Prentice Hall.Google Scholar
- R. Meyer, J. Faber, J. Hoenicke, and A. Rybalchenko. 2008. Model checking Duration Calculus: a practical approach. Formal Aspects of Computing 20, 4 (2008), 481--505. Google ScholarCross Ref
- P. K. Pandya. 2001. Specifying and deciding quantified discrete-time duration calculus formulae using DCVALID. In RT-TOOLS 2001.Google Scholar
- W. L. Pearn, S. H. Chung, A. Y. Chen, and M. H. Yang. 2004. A case study on the multistage IC final testing scheduling problem with reentry. International J. of Production Economics 88, 3 (2004), 257 - 267.Google ScholarCross Ref
- P. Pettersson. 1999. Modelling and Verification of Real-Time Systems Using Timed Automata: Theory and Practice. PhD thesis. Uppsala University.Google Scholar
- T. G. Rokicki. 1993. Representing and Modeling Digital Circuits. PhD thesis. Stanford University. Google ScholarDigital Library
- B. Sharma, P. K. Pandya, and S. Chakraborty. 2005. Bounded validity checking of interval duration logic. In TACAS 2005. 301--316. Google ScholarDigital Library
- A. Tarski. 1951. A Decision Method for Elementary Algebra and Geometry. University of California Press, Berkeley.Google Scholar
- P. Thai and D. Hung. 2004. Verifying linear duration constraints of timed automata. In ICTAC 2004. 295--309. Google ScholarDigital Library
- M. Zhang, D. Hung, and Z. Liu. 2008. Verification of LDIs by model checking CTL properties. In ICTAC 2008. 395--409. Google ScholarDigital Library
- M. Zhang, Z. Liu, and N. Zhan. 2009. Model checking linear duration invariants of networks of automata. In FSEN 2009. 244--259. Google ScholarDigital Library
- C. Zhou and M. R. Hansen. 2004. Duration Calculus: A Formal Approach to Real-Time Systems. Springer. Google ScholarDigital Library
- C. Zhou, M. R. Hansen, and P. Sestoft. 1993. Decidability and undecidability results for duration calculus. In STACS 1993. 58--68. Google ScholarDigital Library
- C. Zhou, J. Zhang, L. Yang, and X. Li. 1994. Linear duration invariants. In FTRTFT 1994. 86--109. Google ScholarDigital Library
- Q. Zu, M. Zhang, J. Zhu, and N. Zhan. 2013. Bounded model-checking of discrete duration calculus. In HSCC 2013. 213--222. Google ScholarDigital Library
Index Terms
- Model Checking Bounded Continuous-time Extended Linear Duration Invariants
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