Incremental DFA Minimisation

  • Marco Almeida
  • Nelma Moreira
  • Rogério Reis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6482)


We present a new incremental algorithm for minimising deterministic finite automata. It runs in quadratic time for any practical application and may be halted at any point, returning a partially minimised automaton. Hence, the algorithm may be applied to a given automaton at the same time as it is processing a string for acceptance. We also include some experimental comparative results.


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  1. [AAA+09]
    Almeida, A., Almeida, M., Alves, J., Moreira, N., Reis, R.: FAdo and GUItar: tools for automata manipulation and visualization. In: Maneth, S. (ed.) CIAA 2009. LNCS, vol. 5642, pp. 65–74. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. [AMR07]
    Almeida, M., Moreira, N., Reis, R.: Enumeration and generation with a string automata representation. Theoret. Comput. Sci. 387(2), 93–102 (2007); Special issue Selected papers of DCFS 2006MathSciNetCrossRefMATHGoogle Scholar
  3. [Brz63]
    Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. In: Fox, J. (ed.) Proc. of the Sym. on Math. Theory of Automata, NY. MRI Symposia Series, vol. 12, pp. 529–561 (1963)Google Scholar
  4. [CLRS03]
    Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms. MIT, Cambridge (2003)MATHGoogle Scholar
  5. [FAd10]
    Project FAdo. FAdo: tools for formal languages manipulation, (access date:1.1.2010)
  6. [HMU00]
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison Wesley, Reading (2000)MATHGoogle Scholar
  7. [Hop71]
    Hopcroft, J.: An nlogn algorithm for minimizing states in a finite automaton. In: Proc. Inter. Symp. on the Theory of Machines and Computations, Haifa, Israel, pp. 189–196. Academic Press, London (1971)CrossRefGoogle Scholar
  8. [Huf55]
    Huffman, D.A.: The synthesis of sequential switching circuits. The Journal of Symbolic Logic 20(1), 69–70 (1955)MathSciNetGoogle Scholar
  9. [Moo58]
    Moore, E.F.: Gedanken-experiments on sequential machines. The Journal of Symbolic Logic 23(1), 60 (1958)Google Scholar
  10. [Tar75]
    Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. JACM 22(2), 215–225 (1975)MathSciNetCrossRefMATHGoogle Scholar
  11. [Wat95]
    Watson, B.W.: Taxonomies and toolkit of regular languages algortihms. PhD thesis, Eindhoven Univ. of Tec. (1995)Google Scholar
  12. [Wat01]
    Watson, B.W.: An incremental DFA minimization algorithm. In: International Workshop on Finite-State Methods in Natural Language Processing, Helsinki, Finland (August 2001)Google Scholar
  13. [WD03]
    Watson, B.W., Daciuk, J.: An efficient DFA minimization algorithm. Natural Language Engineering, 49–64 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marco Almeida
    • 1
  • Nelma Moreira
    • 1
  • Rogério Reis
    • 1
  1. 1.DCC-FC & LIACCUniversidade do PortoPortoPortugal

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