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Implementation of State Elimination Using Heuristics

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Book cover Implementation and Application of Automata (CIAA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5642))

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Abstract

State elimination is an intuitive and easy-to-implement algorithm that computes a regular expression from a finite-state automaton (FA). The size of a regular expression from state elimination depends on the state removal sequence. Note that it is very hard to compute the shortest regular expression for a given FA in general and we cannot avoid the exponential blow-up from state elimination. Nevertheless, we notice that we may have a shorter regular expression if we choose a good removal sequence. This observation motivates us to examine heuristics based on the structural properties of an FA and implement state elimination using the heuristics that run in polynomial time. We demonstrate the effectiveness of our algorithm by experiments.

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References

  1. Brüggemann-Klein, A., Wood, D.: One-unambiguous regular languages. Information and Computation 140, 229–253 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brzozowski, J., McCluskey Jr., E.: Signal flow graph techniques for sequential circuit state diagrams. IEEE Transactions on Electronic Computers EC-12, 67–76 (1963)

    Article  MATH  Google Scholar 

  3. Delgado, M., Morais, J.: Approximation to the smallest regular expression for a given regular language. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds.) CIAA 2004. LNCS, vol. 3317, pp. 312–314. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Ellul, K., Krawetz, B., Shallit, J., Wang, M.-W.: Regular expressions: New results and open problems. Journal of Automata, Languages and Combinatorics 9, 233–256 (2004)

    MathSciNet  MATH  Google Scholar 

  5. Glushkov, V.: The abstract theory of automata. Russian Mathematical Surveys 16, 1–53 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gruber, H., Holzer, M.: Provably shorter regular expressions from deterministic finite automata. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol. 5257, pp. 383–395. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Gulan, S., Fernau, H.: Local elimination-strategies in automata for shorter regular expressions. In: Proceedings of SOFSEM 2008, pp. 46–57 (2008)

    Google Scholar 

  8. Han, Y.-S., Wood, D.: Obtaining shorter regular expressions from finite-state automata. Theoretical Computer Science 370(1-3), 110–120 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation, 2nd edn. Addison-Wesley, Reading (1979)

    MATH  Google Scholar 

  10. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM Journal on Computing 22(6), 1117–1141 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  11. Kleene, S.: Representation of events in nerve nets and finite automata. In: Shannon, C., McCarthy, J. (eds.) Automata Studies, pp. 3–42. Princeton University Press, Princeton (1956)

    Google Scholar 

  12. McNaughton, R., Yamada, H.: Regular expressions and state graphs for automata. IEEE Transactions on Electronic Computers 9, 39–47 (1960)

    Article  MATH  Google Scholar 

  13. Meyer, A., Stockmeyer, L.: The equivalence problem for regular expressions with squaring requires exponential time. In: Proceedings of the Thirteenth Annual IEEE Symposium on Switching and Automata Theory, pp. 125–129 (1972)

    Google Scholar 

  14. Moreira, N., Reis, R.: Series-parallel automata and short regular expressions. Fundamenta Informaticae (accepted for publication, 2009)

    Google Scholar 

  15. Rodger, S.H., Finley, T.W.: JFLAP: An Interactive Formal Languages and Automata Package. Jones & Bartlett Pub. (2006)

    Google Scholar 

  16. Thompson, K.: Regular expression search algorithm. Communications of the ACM 11, 419–422 (1968)

    Article  MATH  Google Scholar 

  17. Wood, D.: Theory of Computation. John Wiley & Sons, Inc., New York (1987)

    MATH  Google Scholar 

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Ahn, JH., Han, YS. (2009). Implementation of State Elimination Using Heuristics. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_21

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  • DOI: https://doi.org/10.1007/978-3-642-02979-0_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02978-3

  • Online ISBN: 978-3-642-02979-0

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