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Tightening the Exchange Rates Between Automata

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Computer Science Logic (CSL 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4646))

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Abstract

Automata on infinite objects were the key to the solution of several fundamental decision problems in mathematics and logic. Today, automata on infinite objects are used for formal specification and verification of reactive systems. The practical importance of automata in formal methods has motivated a re-examination of the blow up that translations among different types of automata involve. For most translations, the situation is satisfying, in the sense that even if there is a gap between the upper and the lower bound, it is small. For some highly practical cases, however, the gap between the upper and the lower bound is exponential or even larger. The article surveys several such frustrating cases, studies features that they share, and describes recent efforts (with partial success) to close the gaps.

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References

  1. Alpern, B., Schneider, F.B.: Defining liveness. IPL 21, 181–185 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Aminof, B., Kupferman, O.: On the succinctness of nondeterminizm. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 125–140. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Büchi, J.R.: On a decision method in restricted second order arithmetic. In: Proc. Int. Congress on Logic, Method, and Philosophy of Science. 1960, pp. 1–12. Stanford University Press (1962)

    Google Scholar 

  4. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. I&C 98(2), 142–170 (1992)

    MATH  MathSciNet  Google Scholar 

  5. Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)

    Google Scholar 

  6. Courcoubetis, C., Vardi, M.Y., Wolper, P., Yannakakis, M.: Memory efficient algorithms for the verification of temporal properties. FMSD 1, 275–288 (1992)

    Google Scholar 

  7. Eisner, C., Fisman, D.: A Practical Introduction to PSL. Springer, Heidelberg (2006)

    Google Scholar 

  8. Emerson, A.E., Sistla, A.P.: Deciding full branching time logics. I&C 61(3), 175–201 (1984)

    MATH  MathSciNet  Google Scholar 

  9. Emerson, E.A.: Alternative semantics for temporal logics. TCS 26, 121–130 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  10. Emerson, E.A., Jutla, C.: The complexity of tree automata and logics of programs. In: Proc. 29th FOCS, pp. 328–337 (1988)

    Google Scholar 

  11. Friedgut, E., Kupferman, O., Vardi, M.Y.: Büchi complementation made tighter. In: Wang, F. (ed.) ATVA 2004. LNCS, vol. 3299, pp. 64–78. Springer, Heidelberg (2004)

    Google Scholar 

  12. Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Protocol Specification, Testing, and Verification, pp. 3–18. Chapman & Hall, Sydney, Australia (1995)

    Google Scholar 

  13. Krishnan, S.C., Puri, A., Brayton, R.K.: Deterministic ω-automata vis-a-vis deterministic Büchi automata. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 378–386. Springer, Heidelberg (1994)

    Google Scholar 

  14. Kupferman, O., Lampert, R.: On the construction of fine automata for safety properties. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 110–124. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Kupferman, O., Morgenstern, G., Murano, A.: Typeness for ω-regular automata. In: Wang, F. (ed.) ATVA 2004. LNCS, vol. 3299, pp. 324–338. Springer, Heidelberg (2004)

    Google Scholar 

  16. Kupferman, O., Vardi, M.Y.: Model checking of safety properties. FMSD 19(3), 291–314 (2001)

    MATH  MathSciNet  Google Scholar 

  17. Kupferman, O., Vardi, M.Y.: From linear time to branching time. ACM TOCL 6(2), 273–294 (2005)

    Article  MathSciNet  Google Scholar 

  18. Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: Proc. 46th FOCS, pp. 531–540 (2005)

    Google Scholar 

  19. Kurshan, R.P.: Computer Aided Verification of Coordinating Processes. Princeton Univ. Press, Princeton (1994)

    Google Scholar 

  20. Lamport, L.: Logical foundation. In: Alford, M.W., Hommel, G., Schneider, F.B., Ansart, J.P., Lamport, L., Mullery, G.P., Liskov, B. (eds.) Distributed Systems. LNCS, vol. 190, Springer, Heidelberg (1985)

    Google Scholar 

  21. Landweber, L.H.: Decision problems for ω–automata. Mathematical Systems Theory 3, 376–384 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  22. Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: Proc. 12th POPL, pp. 97–107 (1985)

    Google Scholar 

  23. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1992)

    Google Scholar 

  24. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Safety. Springer, Heidelberg (1995)

    Google Scholar 

  25. McNaughton, R.: Testing and generating infinite sequences by a finite automaton. I&C 9, 521–530 (1966)

    MATH  MathSciNet  Google Scholar 

  26. Meyer, A.R.: Weak monadic second order theory of successor is not elementary recursive. In: AUSCRYPT 1990. LNM 453, pp. 132–154. Springer, Heidelberg (1975)

    Chapter  Google Scholar 

  27. Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: Proc. 12th SWAT, pp. 188–191 (1971)

    Google Scholar 

  28. Michel, M.: Complementation is more difficult with automata on infinite words. CNET, Paris (1988)

    Google Scholar 

  29. Pnueli, A.: The temporal semantics of concurrent programs. TCS 13, 45–60 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  30. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proc. 16th POPL, pp. 179–190 (1989)

    Google Scholar 

  31. Rabin, M.O.: Decidability of second order theories and automata on infinite trees. Transaction of the AMS 141, 1–35 (1969)

    Article  MATH  MathSciNet  Google Scholar 

  32. Ravi, K., Bloem, R., Somenzi, F.: A comparative study of symbolic algorithms for the computation of fair cycles. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 143–160. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  33. Safra, S.: On the complexity of ω-automata. In: Proc. 29th FOCS, pp. 319–327 (1988)

    Google Scholar 

  34. Sistla, A.P.: Safety, liveness and fairness in temporal logic. Formal Aspects of Computing 6, 495–511 (1994)

    Article  MATH  Google Scholar 

  35. Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logic. JACM 32, 733–749 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  36. Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. In: Brauer, W. (ed.) Automata, Languages and Programming. LNCS, vol. 194, pp. 465–474. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  37. Street, R.S., Emerson, E.A.: An elementary decision procedure for the μ-calculus. In: Paredaens, J. (ed.) Automata, Languages, and Programming. LNCS, vol. 172, pp. 465–472. Springer, Heidelberg (1984)

    Google Scholar 

  38. Touati, H.J., Brayton, R.K., Kurshan, R.: Testing language containment for ω-automata using BDD’s. I&C 118(1), 101–109 (1995)

    MATH  MathSciNet  Google Scholar 

  39. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. 1st LICS, pp. 332–344 (1986)

    Google Scholar 

  40. Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. JCSS 32(2), 182–221 (1986)

    MathSciNet  Google Scholar 

  41. Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. I&C 115(1), 1–37 (1994)

    MATH  MathSciNet  Google Scholar 

  42. Wilke, T.: CTL +  is exponentially more succinct than CTL. In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 1738, pp. 110–121. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  43. Wolper, P., Vardi, M.Y., Sistla, A.P.: Reasoning about infinite computation paths. In: Proc. 24th FOCS, pp. 185–194 (1983)

    Google Scholar 

  44. Yan, Q.: Lower bounds for complementation of ω-automata via the full automata technique. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 589–600. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. School of Computer Science and Engineering, Hebrew University, Jerusalem 91904, Israel

    Orna Kupferman

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  1. Orna Kupferman
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Jacques Duparc Thomas A. Henzinger

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Kupferman, O. (2007). Tightening the Exchange Rates Between Automata. In: Duparc, J., Henzinger, T.A. (eds) Computer Science Logic. CSL 2007. Lecture Notes in Computer Science, vol 4646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74915-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-74915-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74914-1

  • Online ISBN: 978-3-540-74915-8

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