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Minimal Unambiguous εNFA

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Implementation and Application of Automata (CIAA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3317))

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Abstract

A nondeterministic finite automaton with ε-transitions(εNFA) accepts a regular language. Among the εNFA accepting a certain language some are more compact than others. This essay treats the problem of how to compactify a given εNFA by reducing the number of transitions. Compared to the standard techniques to minimize deterministic complete finite automata (complete DFA) two novel features matter in compactifying εNFA: the principle of transition partition and the principle of transition union. An algorithm for compactifying εNFA is presented that exploits the union principle. This algorithm has the following property: if the algorithm returns an unambiguous automaton, then this automaton is the transition minimal εNFA.

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References

  1. Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Anlalysis of Computer Algorithms. Addison-Wesley, Reading (1974)

    Google Scholar 

  2. Arnold, A., Dicky, A., Nivat, M.: A note about minimal non-deterministic automata. Bulletin of the European Association for Theoretical Computer Science 47, 166–169 (1992)

    MATH  Google Scholar 

  3. Brauer, W.: Automatentheorie. Teuber, Stuttgart (1984)

    Google Scholar 

  4. Brauer, W.: On minimizing finite automata. Bulletin of the European Assciation for Theoretical Computer Science (EATCS) 35, 113–116 (1988)

    MATH  Google Scholar 

  5. Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. In: Mathematical Theory of Automata, pp. 529–561. Polytechnic Press, Polytechnic Institute of Brooklyn (1962)

    Google Scholar 

  6. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. W.H. Freeman and Co., New York (1979)

    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.: An n log n algorithm for minimizing states in a finite automaton. In: Proc. International Symposium on Theory of Machines and Computations, Technion, Haifa (IL), pp. 189–196 (1971)

    Google Scholar 

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

    MATH  Google Scholar 

  10. Huffman, D.A.: The synthesis of sequential switching circuits. Journal of the Franklin Institute 257(3-4), 161–190, 275–303 (1954)

    Article  MathSciNet  Google Scholar 

  11. John, S.: Minimal unambiguous eNFA. Technical report, TR-2003-22, Technical University Berlin

    Google Scholar 

  12. Kameda, T., Weiner, P.: On the state minimization of nondeterministic finite automata. IEEE Transactions on Computers C-19, 617–627 (1970)

    Article  MathSciNet  Google Scholar 

  13. Kim, J.: State minimization of nondeterministic machines. Technical report, RC 4896, IBM Thomas J. Watson Research Center (1974)

    Google Scholar 

  14. Matz, O., Potthoff, A.: Computing small nondeterministic finite automata. In: Proc. Workshop on Tools and Algorithms for the Construction and Analysis of Systems, pp. 74–88 (1995)

    Google Scholar 

  15. Mealy, G.H.: Method for synthesizing sequential circuits. Bell System Technical Journal 34, 1045–1079 (1955)

    MathSciNet  Google Scholar 

  16. Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: Proc. 12th Annual Symposium on Switching and Automata Theory, pp. 188–191 (1971)

    Google Scholar 

  17. Moore, E.F.: Gedanken-experiments on sequential machines. Automata Studies, Annals of Mathematics Series 34, 129–153 (1956)

    Google Scholar 

  18. Myhill, J.: Finite automata and the representation of events. Technical report, WADC TR-57-624, Wright Patterson Air Force Base, Ohio, USA (1957)

    Google Scholar 

  19. Nerode, A.: Linear automaton transformations. Proc. American Mathematical Society 9, 514–544 (1958)

    MathSciNet  Google Scholar 

  20. Neuber, S., Starke, P.H.: Über Homomorphie und Reduktion bei nicht-deterministischen Automaten. EIK: Elektronische Informationsverarbeitung und Kybernetik 3, 351–362 (1967)

    MATH  MathSciNet  Google Scholar 

  21. Rabin, M.O., Scott, D.S.: Finite automata and their decision problems. IBM Journal of Research and Development 3, 114–125 (1959)

    Article  MathSciNet  Google Scholar 

  22. Ravikumar, B., Ibarra, O.H.: Relating the type of ambiguity of finite automata to the succinctness of their representation. SIAM Journal on Computing 18(6), 1263–1282 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  23. Schmidt, E.M.: Succinctness of descriptions of context-free, regular, and finite languages. Technical Report DAIMI PB-84, Department of Computer Science, University of Aarhus, Denmark (1978)

    Google Scholar 

  24. Sippu, S., Soisalon-Soininen, E.: Parsing Theory. Languages and Parsing. EATCS Monographs on Theoretical Computer Science, vol. I. Springer, Heidelberg (1988)

    MATH  Google Scholar 

  25. Starke, P.H.: Einige Bemerkungen über nicht-deterministische Automaten. EIK: Elektronische Informationsverarbeitung und Kybernetik 2, 61–82 (1966)

    MATH  MathSciNet  Google Scholar 

  26. Stearns, R.E., Hunt III, H.B.: On the equivalence and containment problems for unambiguous regular expressions, grammars, and automata. In: IEEE: 22nd Annual Symposium on Foundations of Computer Science, pp. 74–81 (1981)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Science, Technical University Berlin, iv,  

    Sebastian John

Authors
  1. Sebastian John
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Editors and Affiliations

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

    Michael Domaratzki

  2. Department of Mathematics, University of Turku, Finland

    Alexander Okhotin

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

    Kai Salomaa

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

    Sheng Yu

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© 2005 Springer-Verlag Berlin Heidelberg

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John, S. (2005). Minimal Unambiguous εNFA. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_18

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  • DOI: https://doi.org/10.1007/978-3-540-30500-2_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24318-2

  • Online ISBN: 978-3-540-30500-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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