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Alternation Elimination for Automata over Nested Words

  • Christian Dax
  • Felix Klaedtke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6604)

Abstract

This paper presents constructions for translating alternating automata into nondeterministic nested-word automata (NWAs). With these alternation-elimination constructions at hand, we straightforwardly obtain translations from various temporal logics over nested words from the literature like CaRet and μNWTL, and extensions thereof to NWAs, which correct, simplify, improve, and generalize the previously given translations. Our alternation-elimination constructions are instances of an alternation-elimination scheme for automata that operate over the tree unfolding of graphs. We obtain these instances by providing constructions for complementing restricted classes of automata with respect to the graphs given by nested words. The scheme generalizes our alternation-elimination scheme for word automata and the presented complementation constructions generalize existing complementation constructions for word automata.

References

  1. 1.
    IEEE standard for property specification language (PSL). IEEE Std 1850TM (October 2005)Google Scholar
  2. 2.
    Alur, R., Arenas, M., Barceló, P., Etessami, K., Immerman, N., Libkin, L.: First-order and temporal logics for nested words. Log. Methods Comput. Sci. 4(4) (2008)Google Scholar
  3. 3.
    Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T.W., Yannakakis, M.: Analysis of recursive state machines. ACM Trans. Progr. Lang. Syst. 27(4), 786–818 (2005)CrossRefGoogle Scholar
  4. 4.
    Alur, R., Etessami, K., Madhusudan, P.: A temporal logic of nested calls and returns. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 467–481. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: ACM Symposium on Theory of Computing (STOC), pp. 202–211. ACM Press, New York (2004)Google Scholar
  6. 6.
    Alur, R., Madhusudan, P.: Adding nesting structure to words. J. ACM 56(3), 1–43 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ball, T., Rajamani, S.K.: Boolean programs: A model and process for software analysis. Technical Report MSR-TR-2000-14, Microsoft Research (2000)Google Scholar
  8. 8.
    Banieqbal, B., Barringer, H.: Temporal logic with fixed points. In: Banieqbal, B., Pnueli, A., Barringer, H. (eds.) Temporal Logic in Specification. LNCS, vol. 398, pp. 62–74. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  9. 9.
    Ben-David, S., Bloem, R., Fisman, D., Griesmayer, A., Pill, I., Ruah, S.: Automata construction algorithms optimized for PSL. Technical report, The Prosyd Project (2005), http://www.prosyd.org
  10. 10.
    Bozzelli, L.: Alternating automata and a temporal fixpoint calculus for visibly pushdown languages. In: Caires, L., Li, L. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 476–491. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Dax, C., Klaedtke, F.: Alternation elimination by complementation. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 214–229. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Dax, C., Klaedtke, F., Lange, M.: On regular temporal logics with past. Acta Inform. 47(4), 251–277 (2010)CrossRefGoogle Scholar
  13. 13.
    Kupferman, O., Vardi, M.Y.: Weak alternating automata are not that weak. ACM Trans. Comput. Log. 2(3), 408–429 (2001)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kupferman, O., Vardi, M.Y.: Complementation constructions for nondeterministic automata on infinite words. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 206–221. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Lange, M.: Linear time logics around PSL: Complexity, expressiveness, and a little bit of succinctness. In: Caires, L., Li, L. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 90–104. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Miyano, S., Hayashi, T.: Alternating finite automata on ω-words. Theoret. Comput. Sci. 32(3), 321–330 (1984)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Muller, D., Saoudi, A., Schupp, P.: Alternating automata, the weak monadic theory of trees and its complexity. Theoret. Comput. Sci. 97(2), 233–244 (1992)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Muller, D., Schupp, P.: Alternating automata on infinite trees. Theoret. Comput. Sci. 54(2–3), 267–276 (1987)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM Journal of Research and Development 3(2), 198–200 (1959)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Vardi, M.Y.: A temporal fixpoint calculus. In: ACM Symposium on Principles of Programming Languages (POPL), pp. 250–259. ACM Press, New York (1988)CrossRefGoogle Scholar
  21. 21.
    Vardi, M.Y.: A note on the reduction of two-way automata to one-way automata. Inform. Process. Lett. 30(5), 261–264 (1989)MathSciNetCrossRefGoogle Scholar
  22. 22.
    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)CrossRefGoogle Scholar
  23. 23.
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Symposium on Logic in Computer Science (LICS), pp. 332–344. IEEE Computer Society, Los Alamitos (1986)Google Scholar
  24. 24.
    Wolper, P.: Temporal logic can be more expressive. Information and Control 56(1-2), 72–99 (1983)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Christian Dax
    • 1
  • Felix Klaedtke
    • 1
  1. 1.Computer Science DepartmentETH ZurichSwitzerland

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