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State Complexity of Catenation Combined with Union and Intersection

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Implementation and Application of Automata (CIAA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6482))

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Abstract

In this paper, we study the state complexities of two particular combinations of operations: catenation combined with union and catenation combined with intersection. We show that the state complexity of the former combined operation is considerably less than the mathematical composition of the state complexities of catenation and union, while the state complexity of the latter one is equal to the mathematical composition of the state complexities of catenation and intersection.

All correspondence should be directed to Yuan Gao at ygao72@csd.uwo.ca. This work is supported by Natural Science and Engineering Council of Canada Discovery Grant R2824A01, Canada Research Chair Award, and Natural Science and Engineering Council of Canada Discovery Grant 41630.

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References

  1. Campeanu, C., Culik, K., Salomaa, K., Yu, S.: State complexity of basic operations on finite language. In: Boldt, O., Jürgensen, H. (eds.) WIA 1999. LNCS, vol. 2214, pp. 60–70. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  2. Domaratzki, M., Okhotin, A.: State complexity of power. Theoretical Computer Science 410(24-25), 2377–2392 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ésik, Z., Gao, Y., Liu, G., Yu, S.: Estimation of state complexity of combined operations. Theoretical Computer Science 410(35), 3272–3280 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gao, Y., Salomaa, K., Yu, S.: The state complexity of two combined operations: star of catenation and star of Reversal. Fundam. Inform. 83(1-2), 75–89 (2008)

    MathSciNet  MATH  Google Scholar 

  5. Gao, Y., Yu, S.: State complexity approximation. In: Proceedings of Descriptional Complexity of Formal Systems, pp. 163–174 (2009)

    Google Scholar 

  6. Han, Y., Salomaa, K.: State complexity of basic operations on suffix-free regular languages. Theoretical Computer Science 410(27-29), 2537–2548 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Holzer, M., Kutrib, M.: State complexity of basic operations on nondeterministic finite automata. In: Champarnaud, J.-M., Maurel, D. (eds.) CIAA 2002. LNCS, vol. 2608, pp. 148–157. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  8. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Reading (1979)

    MATH  Google Scholar 

  9. Jirásek, J., Jirásková, G., Szabari, A.: State complexity of concatenation and complementation of regular languages. International Journal of Foundations of Computer Science 16, 511–529 (2005)

    Article  MATH  Google Scholar 

  10. Jirásková, G.: State complexity of some operations on binary regular languages. Theoretical Computer Science 330, 287–298 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jirásková, G., Okhotin, A.: On the state complexity of star of union and star of intersection. Turku Center for Computer Science TUCS Technical Report No. 825 (2007)

    Google Scholar 

  12. Liu, G., Martin-Vide, C., Salomaa, A., Yu, S.: State complexity of basic language operations combined with reversal. Information and Computation 206, 1178–1186 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  14. Salomaa, A., Wood, D., Yu, S.: On the state complexity of reversals of regular languages. Theoretical Computer Science 320, 293–313 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Salomaa, A., Salomaa, K., Yu, S.: State complexity of combined operations. Theoretical Computer Science 383, 140–152 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu, S., Zhuang, Q., Salomaa, K.: The state complexity of some basic operations on regular languages. Theoretical Computer Science 125, 315–328 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  17. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  18. Yu, S.: State complexity of regular languages. Journal of Automata, Languages and Combinatorics 6(2), 221–234 (2001)

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, London, Ontario, Canada, N6A 5B7

    Bo Cui, Yuan Gao, Lila Kari & Sheng Yu

Authors
  1. Bo Cui
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  2. Yuan Gao
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  3. Lila Kari
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  4. Sheng Yu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, MB, Canada

    Michael Domaratzki

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

    Kai Salomaa

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Cui, B., Gao, Y., Kari, L., Yu, S. (2011). State Complexity of Catenation Combined with Union and Intersection. In: Domaratzki, M., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2010. Lecture Notes in Computer Science, vol 6482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18098-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-18098-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18097-2

  • Online ISBN: 978-3-642-18098-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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