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Deciding Determinism of Unary Languages Is coNP-Complete

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Developments in Language Theory (DLT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7907))

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Abstract

In this paper, we give the complexity of deciding determinism of unary languages. First, we derive a set of arithmetic progressions from an expression E over a unary alphabet, and give the relations between numbers in these arithmetic progressions and words in L(E). Next, we define a problem related to arithmetic progressions and investigate the complexity of this problem. Finally, by reduction from this problem we show that deciding determinism of unary languages is coNP-complete.

Work supported by the National Natural Science Foundation of China under Grant No. 61070038.

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References

  1. Bex, G.J., Gelade, W., Martens, W., Neven, F.: Simplifying XML schema: effortless handling of nondeterministic regular expressions. In: SIGMOD 2009, pp. 731–743 (2009)

    Google Scholar 

  2. Bickel, K., Firrisa, M., Ortiz, J., Pueschel, K.: Constructions of Coverings of the Integers: Exploring an Erdős problem. Summer Math Institute, Cornell University (2008)

    Google Scholar 

  3. Brüggemann-Klein, A.: Regular expressions into finite automata. Theoretical Computer Science 120(2), 197–213 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Information and Computation 142(2), 182–206 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, H., Lu, P.: Assisting the Design of XML Schema: Diagnosing Nondeterministic Content Models. In: Du, X., Fan, W., Wang, J., Peng, Z., Sharaf, M.A. (eds.) APWeb 2011. LNCS, vol. 6612, pp. 301–312. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  7. Erdős, P.: On integers of the form 2k + p and some related problems. Summa Brasil. Math. 2, 113–123 (1950)

    MathSciNet  Google Scholar 

  8. Garrey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman (1979)

    Google Scholar 

  9. Gelade, W., Gyssens, M., Martens, W.: Regular expressions with counting: weak versus strong determinism. SIAM J. Comput. 41(1), 160–190 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics: a foundation for computer science, 2nd edn. Addison-Wesley (1994)

    Google Scholar 

  11. Groz, B., Maneth, S., Staworko, S.: Deterministic regular expressions in linear time. In: PODS 2012, pp. 49–60 (2012)

    Google Scholar 

  12. Guy, R.K.: Unsolved problems in Number Theory, 3rd edn. Problem Books in Math. Springer, New York (2004)

    Book  MATH  Google Scholar 

  13. Holzer, M., Kutrib, M.: The complexity of regular(-like) expressions. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 16–30. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Kilpeläinen, P.: Checking determinism of XML Schema content models in optimal time. Informat. Systems 36(3), 596–617 (2011)

    Article  Google Scholar 

  15. Losemann, K., Martens, W., Niewerth, M.: Descriptional complexity of deterministic regular expressions. In: Rovan, B., Sassone, V., Widmayer, P. (eds.) MFCS 2012. LNCS, vol. 7464, pp. 643–654. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  16. Sawa, Z.: Efficient construction of semilinear representations of languages accepted by unary NFA. In: Kučera, A., Potapov, I. (eds.) RP 2010. LNCS, vol. 6227, pp. 176–182. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  17. Schnitger, G.: Regular expressions and NFAs without ε-transitions. In: Durand, B., Thomas, W. (eds.) STACS 2006. LNCS, vol. 3884, pp. 432–443. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Steen, L.A., Seebach, J.A.: Counterexamples in topology, 2nd edn. Springer, New York (1978)

    Book  MATH  Google Scholar 

  19. Stockmeyer, L.J., Meyer, A.R.: Word problems requiring exponential time: preliminary report. In: STOC 1973, pp. 1–9 (1973)

    Google Scholar 

  20. van der Vlist, E.: XML Schema. O’Reilly (2002)

    Google Scholar 

  21. World Wide Web Consortium, http://www.w3.org/wiki/UniqueParticleAttribution

  22. Yu, S., Zhuang, Q., Salomaa, K.: The state complexities of some basic operations on regular langauges. Theoretical Computer Science 125(2), 315–328 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, China

    Ping Lu & Haiming Chen

  2. Graduate University of Chinese Academy of Sciences, China

    Ping Lu

  3. University of Chinese Academy of Sciences, China

    Ping Lu

  4. China Agricultural University, Beijing, 100083, China

    Feifei Peng

Authors
  1. Ping Lu
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  2. Feifei Peng
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  3. Haiming Chen
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Editor information

Editors and Affiliations

  1. LIGM, University Paris-Est Marne-la-Vallée, 5 Bd Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Marie-Pierre Béal

  2. LIAFA, UMR 7089, University Paris Diderot, 75205, Paris cedex 13, France

    Olivier Carton

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Lu, P., Peng, F., Chen, H. (2013). Deciding Determinism of Unary Languages Is coNP-Complete. In: Béal, MP., Carton, O. (eds) Developments in Language Theory. DLT 2013. Lecture Notes in Computer Science, vol 7907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38771-5_31

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  • DOI: https://doi.org/10.1007/978-3-642-38771-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38770-8

  • Online ISBN: 978-3-642-38771-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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