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International Symposium on Mathematical Foundations of Computer Science

MFCS 2011: Mathematical Foundations of Computer Science 2011 pp 485–496Cite as

State Complexity of Operations on Input-Driven Pushdown Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6907))

Abstract

The family of deterministic input-driven pushdown automata (IDPDA; a.k.a. visibly pushdown automata, a.k.a. nested word automata) is known to be closed under reversal, concatenation and Kleene star. As shown by Alur and Madhusudan (``Visibly pushdown languages'', STOC 2004), the reversal and the Kleene star of an n-state IDPDA can be represented by an IDPDA with \(2^{O(n^2)}\) states, while concatenation of an m-state and an n-state IDPDA is represented by an IDPDA with \(2^{O((m+n)^2)}\) states. This paper presents more efficient constructions for the reversal and for the Kleene star, which yield 2Θ(n logn) states, as well as an m 2Θ(n logn)-state construction for the concatenation. These constructions are optimal due to the previously known matching lower bounds.

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References

  1. Alur, R., Kumar, V., Madhusudan, P., Viswanathan, M.: Congruences for visibly pushdown languages. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1102–1114. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  2. Alur, R., Madhusudan, P.: Visibly pushdown languages. In: ACM Symposium on Theory of Computing STOC 2004, Chicago, USA, June 13–16, pp. 202–211 (2004)

    Google Scholar 

  3. Alur, R., Madhusudan, P.: Adding nesting structure to words. Journal of the ACM 56, 3 (2009)

    Article  MathSciNet  Google Scholar 

  4. Birget, J.C.: Partial orders on words, minimal elements of regular languages, and state complexity. Theoretical Computer Science 119, 267–291 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. von Braunmuhl, B., Verbeek, R.: Input-driven languages are recognized in logn space. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 40–51. Springer, Heidelberg (1983)

    Google Scholar 

  6. Chervet, P., Walukiewicz, I.: Minimizing variants of visibly pushdown automata. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 135–146. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Crespi Reghizzi, S., Mandrioli, D.: Operator precedence and the visibly pushdown property. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 214–226. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  8. Domaratzki, M., Okhotin, A.: State complexity of power. Theoretical Computer Science 410, 24–25 (2009)

    Article  MathSciNet  Google Scholar 

  9. Han, Y.-S., Salomaa, K.: Nondeterministic state complexity of nested word automata. Theoretical Computer Science 410, 2961–2971 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. International Journal of Foundations of Computer Science 14, 1087–1102 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Leiss, E.L.: Succinct representation of regular languages by Boolean automata. Theoretical Computer Science 13, 323–330 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  12. Maslov, A.N.: Estimates of the number of states of finite automata. Soviet Mathematics Doklady 11, 1373–1375 (1970)

    MATH  Google Scholar 

  13. Mehlhorn, K.: Pebbling mountain ranges and its application to DCFL-recognition. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 422–435. Springer, Heidelberg (1980)

    Google Scholar 

  14. Okhotin, A.: Unambiguous finite automata over a unary alphabet. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 556–567. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Okhotin, A.: Comparing linear conjunctive languages to subfamilies of the context-free languages. In: Černá, I., Gyimóthy, T., Hromkovič, J., Jefferey, K., Králović, R., Vukolić, M., Wolf, S. (eds.) SOFSEM 2011. LNCS, vol. 6543, pp. 431–443. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Okhotin, A., Salomaa, K.: Descriptional Complexity of Unambiguous Nested Word Automata. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 414–426. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Piao, X., Salomaa, K.: Operational state complexity of nested word automata. Theoretical Computer Science 410, 3290–3302 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  18. Rampersad, N.: The state complexity of L 2 and L k. Information Processing Letters 98, 231–234 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Salomaa, K.: Limitations of lower bound methods for deterministic nested word automata. Information and Computation 209, 580–589 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Alexander Okhotin

  2. Academy of Finland, Finland

    Alexander Okhotin

  3. School of Computing, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    Kai Salomaa

Authors
  1. Alexander Okhotin
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  2. Kai Salomaa
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Editor information

Editors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Filip Murlak  & Piotr Sankowski  & 

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Okhotin, A., Salomaa, K. (2011). State Complexity of Operations on Input-Driven Pushdown Automata. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_44

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  • DOI: https://doi.org/10.1007/978-3-642-22993-0_44

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22992-3

  • Online ISBN: 978-3-642-22993-0

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