Abstract
In this paper, we propose a translation procedure of PLTL (LTL with past modalities) formulas to Büchi automata using two-way very-weak alternating automata (2VWAA) as an intermiediary step. Our main result is an efficient translation of 2VWAA to generalized Büchi automata (GBA).
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References
Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, ch. 16, vol. B, pp. 995–1072. Elsevier Science, Amsterdam (1990)
Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Proc. of PoPL 1980, Las Vegas, pp. 163–173 (November 1980)
Gastin, P., Oddoux, D.: Fast LTL to büchi automata translation. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 53–65. Springer, Heidelberg (2001)
Gastin, P., Oddoux, D.: LTL with past and two-way very-weak alternating automata. Tech. Rep. LIAFA 2003–010, Université Paris 7 (France)
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, Warsaw, Poland, pp. 3–18. Chapman & Hall, Boca Raton (1995)
Kamp, J.A.W.: Tense Logic and the Theory of Linear Order. PhD thesis, University of California, Los Angeles, California (1968)
Kesten, Y., Manna, Z., McGuire, H., Pnueli, A.: A decision algorithm for full propositional temporal logic. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 97–109. Springer, Heidelberg (1993)
Kupferman, O., Piterman, N., Vardi, M.Y.: Extended temporal logic revisited. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 519–535. Springer, Heidelberg (2001)
Laroussinie, F., Markey, N., Schnoebelen, Ph.: Temporal logic with forgettable past. In: Proc. of LICS 2002, pp. 383–392 (2002)
Laroussinie, F., Schnoebelen, P.: A hierarchy of temporal logics with past. Theoretical Computer Science 148, 303–324 (1995)
Lichtenstein, O., Pnueli, A., Zuck, L.D.: The glory of the past. In Proc. of the 3rd Workshop on Logics of Programs. In: Parikh, R. (ed.) Logic of Programs 1985. LNCS, vol. 193, pp. 196–218. Springer, Heidelberg (1985)
Manna, Z., Pnueli, A.: The temporal logic of reactive and concurent systems: Specification. Springer, Heidelberg (1992)
Pnueli, A.: The temporal logic of programs. In: Proc. of FOCS 1977, pp. 46–57 (1977)
Ramakrishna, Y.S., Moser, L.E., Dillon, L.K., Melliar-Smith, P.M., Kutty, G.: An automata theoretic decision procedure for propositional temporal logic with Since and Until. Fundamenta Informaticae 17, 271–282 (1992)
Sistla, A.P., Clarke, E.M.: The complexity of propositional linear time logic. Journal of the Association of Computing Machinery 32, 733–749 (1985)
Vardi, M.Y.: Reasoning about the past with two-way automata. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 628–641. Springer, Heidelberg (1998)
Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification. In: Proc. of LICS 1986, pp. 332–344 (1986)
Vardi, M.Y., Wolper, P.: Reasonning about infinite computations. Information and Computation 115, 1–37 (1994)
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Gastin, P., Oddoux, D. (2003). LTL with Past and Two-Way Very-Weak Alternating Automata. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_38
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DOI: https://doi.org/10.1007/978-3-540-45138-9_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40671-6
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