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Modal Strength Reduction in Quantified Discrete Duration Calculus

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FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3821))

Abstract

QDDC is a logic for specifying quantitative timing properties of reactive systems. An automata theoretic decision procedure for QDDC reduces each formula to a finite state automaton accepting precisely the models of the formula. This construction has been implemented into a validity/model checking tool for QDDC called DCVALID. Unfortunately, the size of the final automaton as well as the intermediate automata which are encountered in the construction can some times be prohibitively large. In this paper, we present some validity preserving transformations to QDDC formulae which result into more efficient construction of the formula automaton and hence reduce the validity checking time. The transformations can be computed in linear time. We provide a theoretical as well as an experimental analysis of the improvements in the formula automaton size and validity checking time due to our transformations.

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References

  1. Buchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik Grundl. Math. 6 (1960)

    Google Scholar 

  2. Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc. 98 (1961)

    Google Scholar 

  3. Chakravorty, G., Pandya, P.K.: Digitizing Interval Duration Logic. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 167–179. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Fränzle, M., Herde, C.: Efficient SAT engines for concise logics: Accelerating proof search for zero-one linear constraint systems. In: Y. Vardi, M., Voronkov, A. (eds.) LPAR 2003. LNCS, vol. 2850, pp. 300–314. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Gonnord, L., Halbwachs, N., Raymond, P.: From Discrete Duration Calculus to Symbolic Automata. In: ENTCS Proceedings of SLAP 2004, Barcelona, Spain (2004)

    Google Scholar 

  6. Hansen, M.R.: Model-Checking Duration Calculus. Formal Aspects of Computing (1994)

    Google Scholar 

  7. Henriksen, J.G., Jensen, J., Jorgensen, M., Klarlund, N., Paige, B., Rauhe, T., Sandholm, A.: Mona: Monadic Second-Order Logic in Practice. In: Brinksma, E., Steffen, B., Cleaveland, W.R., Larsen, K.G., Margaria, T. (eds.) TACAS 1995. LNCS, vol. 1019, Springer, Heidelberg (1996)

    Google Scholar 

  8. Klarlund, N., Møller, A., Schwartzbach, M.I.: MONA Implementation Secrets. In: Yu, S., Păun, A. (eds.) CIAA 2000. LNCS, vol. 2088, pp. 182–194. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  9. Krishna, S.N., Pandya, P.K.: Modal Strength Reduction in QDDC, Technical Report (2005), http://www.cse.iitb.ac.in/~krishnas/fsttcstr.ps

  10. Moszkowski, B.: A Temporal Logic for Multi-Level Reasoning about Hardware. IEEE Computer 18(2) (1985)

    Google Scholar 

  11. Pandya, P.K.: Specifying and Deciding Quantified Discrete-time Duration Calculus Formulae using DCVALID: An Automata Theoretic Approach. In: Proceedings of RTTOOLS 2001, Denmark (2001)

    Google Scholar 

  12. Pandya, P.K.: Model checking CTL*[DC]. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 559–573. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. Sharma, B., Pandya, P.K., Chakraborty, S.: Bounded Validity Checking of Interval Duration Logic. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 301–316. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Skakkebaek, J.U., Sestoft, P.: Checking Validity of Duration Calculus Formulas, Technical Report ID/DTH JUS 3/1, Department of Computer Science, Technical University of Denmark (1994)

    Google Scholar 

  15. Chaochen, Z., Hansen, M.R.: Duration Calculus: A formal approach to realtime systems. Springer, Heidelberg (2004)

    Google Scholar 

  16. Chaochen, Z., Hoare, C.A.R., Ravn, A.P.: A Calculus of Durations. Info. Proc. Letters 40(5) (1991)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Indian Institute of Technology, Bombay, India

    Shankara Narayanan Krishna

  2. Tata Institute of Fundamental Research, India

    Paritosh K. Pandya

Authors
  1. Shankara Narayanan Krishna
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  2. Paritosh K. Pandya
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Editor information

Editors and Affiliations

  1. National Institute of Advanced Studies, Indian Institute of Science Campus, 560012, Bangalore, India

    Sundar Sarukkai

  2. Department of Comp. Sc. & Engg., Indian Institute of Technology Delhi, 110016, New Delhi, India

    Sandeep Sen

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Krishna, S.N., Pandya, P.K. (2005). Modal Strength Reduction in Quantified Discrete Duration Calculus. In: Sarukkai, S., Sen, S. (eds) FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2005. Lecture Notes in Computer Science, vol 3821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11590156_36

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  • DOI: https://doi.org/10.1007/11590156_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30495-1

  • Online ISBN: 978-3-540-32419-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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