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Incremental DFA minimisation∗

Published online by Cambridge University Press:  21 January 2014

Marco Almeida ,
Nelma Moreira  and
Rogério Reis
Marco Almeida
Affiliation:
Faculdade de Ciências, Universidade do Porto ;. mfa@dcc.fc.up.pt,nam@dcc.fc.up.pt,rvr@dcc.fc.up.pt
Nelma Moreira
Affiliation:
Faculdade de Ciências, Universidade do Porto ;. mfa@dcc.fc.up.pt,nam@dcc.fc.up.pt,rvr@dcc.fc.up.pt
Rogério Reis
Affiliation:
Faculdade de Ciências, Universidade do Porto ;. mfa@dcc.fc.up.pt,nam@dcc.fc.up.pt,rvr@dcc.fc.up.pt
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Abstract

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.

Keywords

Regular languagesfinite automataminimisation algorithms
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 2 , April 2014 , pp. 173 - 186
Copyright
© EDP Sciences 2014

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References

A. Almeida, M. Almeida, J. Alves, N. Moreira and R. Reis, FAdo and GUItar: tools for automata manipulation and visualization, in vol. 5642 14th CIAA’09, edited by S. Maneth. Lect. Notes Comput. Sci. Springer (2009) 65–74.
Almeida, M., Moreira, N. and Reis, R., Enumeration and generation with a string automata representation, Special issue Selected papers of DCFS (2006). Theoret. Comput. Sci. 387 (2007) 93–102. Google Scholar
M. Almeida, N. Moreira and R. Reis, Incremental DFA minimisation, in Proc. of the 15th International Conference on Implementation and Application of Automata (CIAA 2010) Winnipeg, MA, Canada, vol. 6482 of Lect. Notes Comput. Sci., edited by M. Domaratzki and K. Salomaa. Springer-Verlag (2010) 39–48.
M. Almeida, Equivalence of regular languages: an algorithmic approach and complexity analysis, Ph.D. thesis. University of Porto (2011).
J.A. Brzozowski, Canonical regular expressions and minimal state graphs for definite events, in vol. 12 of Proc. of the Sym. on Math. Theory of Automata, edited by J. Fox. MRI Symposia Series, New York (1963) 529–561.
T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms. The MIT Press, 2nd edition (2003).
Project FAdo, FAdo: tools for formal languages manipulation. , Access date:1.11.2011 http://fado.dcc.fc.up.pt/, Access date:1.11.2011.
J. Hopcroft, An nlog n algorithm for minimizing states in a finite automaton, in Proc. Inter. Symp. on the Theory of Machines and Computations, Haifa, Israel. Academic Press (1971) 189–196.
J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison Wesley (2000).
Huffman, D.A., The synthesis of sequential switching circuits. J. Symbolic Logic 20 (1955) 69–70. Google Scholar
Moore, E.F., Gedanken-experiments on sequential machines. J. Symbolic Logic 23 (1958) 60. Google Scholar
Tarjan, R.E., Efficiency of a good but not linear set union algorithm. J. ACM 22 (1975) 215–225. Google Scholar
B.W. Watson, Taxonomies and toolkit of regular languages algortihms, Ph.D. thesis. Eindhoven University of Tec. (1995).
B.W. Watson, An incremental DFA minimization algorithm, in International Workshop on Finite-State Methods in Natural Language Processing. Helsinki, Finland (2001).
B.W. Watson and J. Daciuk, An efficient DFA minimization algorithm. Natur. Lang. Engrg. (2003) 49–64.