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State Complexity and Limited Nondeterminism

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Descriptional Complexity of Formal Systems (DCFS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7386))

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Abstract

We consider nondeterministic finite automata having finite tree width (ftw-NFA) where the computation on any input string has a constant number of branches. We give effective characterizations of ftw-NFAs and a tight worst-case state size bound for determinizing an ftw-NFA A as a function of the tree width and the number of states of A. We introduce a lower bound technique for ftw-NFAs and consider the operational state complexity of this model.

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References

  1. Birget, J.C.: Intersection and union of regular languages and state complexity, Inform. Process. Lett. 43, 185–190 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Björklund, H., Martens, W.: The tractability frontier for NFA minimization. J. Comput. System Sci. 78, 198–210 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chrobak, M.: Finite automata and unary languages. Theoret. Comput. Sci. 47, 149–158 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Glaister, I., Shallit, J.: A lower bound technique for the size of nondeterministic finite automata. Inf. Proc. Lett. 59, 75–77 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldstine, J., Kappes, M., Kintala, C.M.R., Leung, H., Malcher, A., Wotschke, D.: Descriptional complexity of machines with limited resources. J. Univ. Comput. Sci. 8, 193–234 (2002)

    MathSciNet  Google Scholar 

  6. Goldstine, J., Kintala, C.M.R., Wotschke, D.: On measuring nondeterminism in regular languages. Inform. Comput. 86, 179–194 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Goldstine, J., Leung, H., Wotschke, D.: On the relation between ambiguity and nondeterminism in finite automata. Inform. Comput. 100, 261–270 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gruber, H., Holzer, M.: Finding Lower Bounds for Nondeterministic State Complexity Is Hard. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 363–374. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Gruber, H., Holzer, M.: Inapproximability of Nondeterministic State and Transition Complexity Assuming P ≠ NP. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 205–216. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Holzer, M., Kutrib, M.: Nondeterministic descriptional complexity of regular languages. Internat. J. Foundations of Comput. Sci. 14, 1087–1102 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  11. Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata — A survey. Inf. Comput. 209, 456–470 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Holzer, M., Salomaa, K., Yu, S.: On the state complexity of k-entry deterministic finite automata. J. Automata, Languages and Combinatorics 6, 453–466 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Hromkovič, J., Seibert, S., Karhumäki, J., Klauck, H., Schnitger, G.: Communication complexity method for measuring nondeterminism in finite automata. Inform. Comput. 172, 202–217 (2002)

    Article  MATH  Google Scholar 

  14. Jiang, T., McDowell, E., Ravikumar, B.: The structure and complexity of minimal NFA’s over a unary alphabet. Internat. J. Foundations Comput. Sci. 2, 163–182 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  15. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22, 1117–1141 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  16. Kappes, M.: Descriptional complexity of deterministic finite automata with multiple initial states. J. Automata, Languages, and Combinatorics 5, 269–278 (2000)

    MathSciNet  MATH  Google Scholar 

  17. Kintala, C.M.R., Wotschke, D.: Amounts of nondeterminism in finite automata. Acta Inform. 13, 199–204 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  18. Leung, H.: Separating exponentially ambiguous finite automata from polynomially ambiguous finite automata. SIAM J. Comput, 1073–1082 (1998)

    Google Scholar 

  19. Leung, H.: Descriptional complexity of NFA of different ambiguity. Internat. J. Foundations Comput. Sci. 16, 975–984 (2005)

    Article  MATH  Google Scholar 

  20. Malcher, A.: Minimizing finite automata is computationally hard. Theoret. Comput. Sci. 327, 375–390 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  21. 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 

  22. Ravikumar, B., Ibarra, O.: Relating the type of ambiguity of finite automata to the succinctness of their representation. SIAM J. Comput. 18, 1263–1282 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  23. Schmidt, E.M.: Succinctness of description of context-free, regular and unambiguous languages. Ph.D. thesis, Cornell University (1978)

    Google Scholar 

  24. Shallit, J.: A Second Course in Formal Languages and Automata Theory. Cambridge University Press (2009)

    Google Scholar 

  25. Stearns, R., Hunt, H.: On the equivalence and containment problems for unambiguous regular expressions, regular grammars and finite automata. SIAM J. Comput. 14, 596–611 (1985)

    Article  MathSciNet  Google Scholar 

  26. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. I, pp. 41–110. Springer (1997)

    Google Scholar 

  27. Yu, S., Zhuang, Q., Salomaa, K.: The state complexity of some basic operations on regular languages. Theoret. Comput. Sci. 125, 315–328 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

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

    Alexandros Palioudakis, Kai Salomaa & Selim G. Akl

Authors
  1. Alexandros Palioudakis
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  2. Kai Salomaa
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  3. Selim G. Akl
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstraße 2, 35392, Giessen, Germany

    Martin Kutrib

  2. Departamento de Ciência de Computadores, Universidade do Porto, Faculdade de Ciências, Rua do Campo Alegre 1021-1055, 4169-007, Porto, Portugal

    Nelma Moreira  & Rogério Reis  & 

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© 2012 Springer-Verlag Berlin Heidelberg

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Palioudakis, A., Salomaa, K., Akl, S.G. (2012). State Complexity and Limited Nondeterminism. In: Kutrib, M., Moreira, N., Reis, R. (eds) Descriptional Complexity of Formal Systems. DCFS 2012. Lecture Notes in Computer Science, vol 7386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31623-4_20

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  • DOI: https://doi.org/10.1007/978-3-642-31623-4_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31622-7

  • Online ISBN: 978-3-642-31623-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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