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International Symposium on Fundamentals of Computation Theory

FCT 2007: Fundamentals of Computation Theory pp 213–225Cite as

Factorization of Fuzzy Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4639))

Abstract

We show that the size reduction problem for fuzzy automata is related to the problem of solving a particular system of fuzzy relation equations. This system consists of infinitely many equations, and finding its general solution is a very difficult task, so we first consider one of its special cases, a finite system whose solutions, called right invariant fuzzy equivalences, are common generalizations of recently studied right invariant or well-behaved equivalences on NFAs, and congruences on fuzzy automata. We give a procedure for constructing the greatest right invariant fuzzy equivalence contained in a given fuzzy equivalence, which work if the underlying structure of truth values is a locally finite residuated lattice.

Research supported by Ministry of Science and Environmental Protection, Republic of Serbia, Grant No. 144011.

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References

  1. Basak, N.C., Gupta, A.: On quotient machines of a fuzzy automation and the minimal machine. Fuzzy Sets and Systems 125, 223–229 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bělohlávek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer, New York (2002)

    MATH  Google Scholar 

  3. Bělohlávek, R.: Determinism of fuzzy automata. Information Sciences 143, 205–209 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Calude, C.S., Calude, E., Khoussainov, B.: Finite nondeterministic automata: Simulation and minimality. Theoretical Computer Science 242, 219–235 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Câmpeanu, C., Sântean, N., Yu, S.: Mergible states in large NFA. Theoretical Computer Science 330, 23–34 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Champarnaud, J.-M., Coulon, F.: NFA reduction algorithms by means of regular inequalities. Theoretical Computer Science 327, 241–253 (2004)

    Article  MathSciNet  Google Scholar 

  7. Cheng, W., Mo, Z.: Minimization algorithm of fuzzy finite automata. Fuzzy Sets and Systems 141, 439–448 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  8. Ćirić, M., Ignjatović, J., Bogdanović, S.: Fuzzy equivalence relations and their equivalence classes. Fuzzy Sets and Systems 158, 1295–1313 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ilie, L., Yu, S.: Algorithms for computing small NFAs. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 328–340. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Ilie, L., Yu, S.: Reducing NFAs by invariant equivalences. Theoretical Computer Science 306, 373–390 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ilie, L., Navarro, G., Yu, S.: On NFA reductions. In: Karhumäki, J., Maurer, H., Păun, G., Rozenberg, G. (eds.) Theory Is Forever. LNCS, vol. 3113, pp. 112–124. Springer, Heidelberg (2004)

    Google Scholar 

  12. Ilie, L., Solis-Oba, R., Yu, S.: Reducing the size of NFAs by using equivalences and preorders. In: Apostolico, A., Crochemore, M., Park, K. (eds.) CPM 2005. LNCS, vol. 3537, pp. 310–321. Springer, Heidelberg (2005)

    Google Scholar 

  13. Lei, H., Li, Y.M.: Minimization of states in automata theory based on finite lattice-ordered monoids. Information Sciences 177, 1413–1421 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Li, Y.M., Pedrycz, W.: Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids. Fuzzy Sets and Systems 156, 68–92 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  15. Malik, D.S., Mordeson, J.N., Sen, M.K.: Minimization of fuzzy finite automata. Information Sciences 113, 323–330 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Mordeson, J.N., Malik, D.S.: Fuzzy Automata and Languages: Theory and Applications. Chapman & Hall/CRC, Boca Raton, London (2002)

    Google Scholar 

  17. Petković, T.: Congruences and homomorphisms of fuzzy automata. Fuzzy Sets and Systems 157, 444–458 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  18. Valverde, L.: On the structure of F-indistinguishability operators. Fuzzy Sets and Systems 17, 313–328 (1985)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia

    Miroslav Ćirić, Aleksandar Stamenković & Jelena Ignjatović

  2. Nokia, Joensuunkatu 7, FIN-24100 Salo, Finland

    Tatjana Petković

Authors
  1. Miroslav Ćirić
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  2. Aleksandar Stamenković
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  3. Jelena Ignjatović
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  4. Tatjana Petković
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Editor information

Erzsébet Csuhaj-Varjú Zoltán Ésik

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© 2007 Springer-Verlag Berlin Heidelberg

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Ćirić, M., Stamenković, A., Ignjatović, J., Petković, T. (2007). Factorization of Fuzzy Automata. In: Csuhaj-Varjú, E., Ésik, Z. (eds) Fundamentals of Computation Theory. FCT 2007. Lecture Notes in Computer Science, vol 4639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74240-1_19

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  • DOI: https://doi.org/10.1007/978-3-540-74240-1_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74239-5

  • Online ISBN: 978-3-540-74240-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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