Abstract
We determine the complexity of topological properties of regular ω-languages (i.e., classes of ω-languages closed under inverse continuous functions). We show that they are typically NL-complete (PSPACE-complete) for the deterministic Muller, Mostowski and Büchi automata (respectively, for the nondeterministic Rabin, Muller, Mostowski and Büchi automata). For the deterministic Rabin and Streett automata and for the nondeterministic Streett automata upper and lower complexity bounds for the topological properties are established.
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References
Balcazar, J.L., Diaz, J., Gabarro, J.: Structural Complextiy I. Springer, Heidelberg (1995)
Cabessa, J.: A Game Theoretic Approach to the Algebraic Counterpart of the Wagner Hierarchy. PhD Thesis, Universities of Lausanne and Paris-7 (2007)
Carton, O., Perrin, D.: Chains and superchains for ω-rational sets, automata and semigroups. International Journal of Algebra and Computation 7(7), 673–695 (1997)
Carton, O., Perrin, D.: The Wagner hierarchy of ω-rational sets. International Journal of Algebra and Computation 9(7), 673–695 (1999)
Duparc, J., Riss, M.: The missing link for ω-rational sets, automata, and semigroups. International Journal of Algebra and Computation 16(1), 161–185 (2006)
Krishnan, S., Puri, A., Brayton, R.: Structural complexity of ω-automata. In: Mosses, P.D., Schwartzbach, M.I., Nielsen, M. (eds.) CAAP 1995, FASE 1995, and TAPSOFT 1995. LNCS, vol. 915, pp. 143–156. Springer, Heidelberg (1995)
Landweber, L.H.: Decision problems for ω-automata. Math. Systems Theory 4, 376–384 (1969)
Löding, C.: Optimal bounds for the transformation of omega-automata. In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 97–109. Springer, Heidelberg (1999)
Meyer, A., Stockmeyer, L.J.: The equivalence problem for regular expressions with squaring requires exponential time. In: Proc. of the 13th IEEE Symp. on Switching and Automata Theory 1972, pp. 125–129 (1972)
Pin, J.-E.: Syntactic semigroups. In: Handbook of Formal Languages, pp. 679–746. Springer, Heidelberg (1997)
Perrin, D., Pin, J.-E.: Infinite Words. Pure and Applied Math, vol. 141. Elsevier, Amsterdam (2004)
Safra, S.: On the complexity of ω-automata. In: Proc. of the 29th IEEE FOCS 1988, pp. 319–327 (1988)
Selivanov, V.L.: Fine hierarchy of regular ω-languages. Theoretical Computer Science 191, 37–59 (1998)
Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for Büchi automata with applications to temporal logic. Theoretical Computer Science 49, 217–237 (1987)
Staiger, L., Wagner, K.: Automatentheoretische und automatenfreie Characterisierungen topologischer Klassen regulärer Folgenmengen. Elektronische Informationsverarbeitung und Kybernetik 10, 379–392 (1974)
Staiger, L.: ω-Languages. In: Handbook of Formal Languages, vol. 3, pp. 339–387. Springer, Heidelberg (1997)
Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, pp. 133–191. Elsevier, Amsterdam (1990)
Thomas, W.: Languages, automata and logic. In: Handbook of Formal Languages, vol. 3, pp. 133–191. Springer, Heidelberg (1997)
Wadge, W.: Degrees of complexity of subsets of the Baire space. Notices AMS 19, 714–715 (1972)
Wadge, W.: Reducibility and determinateness in the Baire space. PhD thesis, University of California, Berkely (1984)
Wagner, K.: On ω-regular sets. Information and Control 43, 123–177 (1979)
Wilke, T.: An algebraic theory for for regular languages of finite and infinite words. Int. J. Alg. Comput. 3, 447–489 (1993)
Wechsung, G.: On the Boolean closure of NP. In: Budach, L. (ed.) FCT 1985. LNCS, vol. 199, pp. 485–493. Springer, Heidelberg (1985)
Wilke, T., Yoo, H.: Computing the Wadge degree, the Lipschitz degree, and the Rabin index of a regular language of infinite words in polynomial time. In: Mosses, P.D., Schwartzbach, M.I., Nielsen, M. (eds.) CAAP 1995, FASE 1995, and TAPSOFT 1995. LNCS, vol. 915, pp. 288–302. Springer, Heidelberg (1995)
Yan, Q.: Lower Bounds for Complementation of omega-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)
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Selivanov, V.L., Wagner, K.W. (2008). Complexity of Topological Properties of Regular ω-Languages. In: Ito, M., Toyama, M. (eds) Developments in Language Theory. DLT 2008. Lecture Notes in Computer Science, vol 5257. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85780-8_42
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DOI: https://doi.org/10.1007/978-3-540-85780-8_42
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