Incremental DFA minimisation
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 173-186.

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.

DOI : https://doi.org/10.1051/ita/2013045
Classification : 68Q45,  68Q65,  68Q25
Mots clés : regular languages, finite automata, minimisation algorithms
@article{ITA_2014__48_2_173_0,
author = {Almeida, Marco and Moreira, Nelma and Reis, Rog\'erio},
title = {Incremental DFA minimisation},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {173--186},
publisher = {EDP-Sciences},
volume = {48},
number = {2},
year = {2014},
doi = {10.1051/ita/2013045},
mrnumber = {3302483},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2013045/}
}
Almeida, Marco; Moreira, Nelma; Reis, Rogério. Incremental DFA minimisation. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 2, pp. 173-186. doi : 10.1051/ita/2013045. http://www.numdam.org/articles/10.1051/ita/2013045/

[1] 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.

[2] M. Almeida, N. Moreira and R. Reis, Enumeration and generation with a string automata representation, Special issue Selected papers of DCFS (2006). Theoret. Comput. Sci. 387 (2007) 93-102. | MR 2362181 | Zbl 1143.68031

[3] 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. | MR 2776275 | Zbl 1297.68103

[4] M. Almeida, Equivalence of regular languages: an algorithmic approach and complexity analysis, Ph.D. thesis. University of Porto (2011).

[5] 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. | MR 175719 | Zbl 0116.33605

[6] T.H. Cormen, C.E. Leiserson, R.L. Rivest and C. Stein, Introduction to Algorithms. The MIT Press, 2nd edition (2003). | MR 1848805 | Zbl 1158.68538

[8] 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. | MR 403320 | Zbl 0293.94022

[9] J.E. Hopcroft, R. Motwani and J.D. Ullman, Introduction to Automata Theory, Languages and Computation. Addison Wesley (2000). | MR 645539 | Zbl 0980.68066

[10] D.A. Huffman, The synthesis of sequential switching circuits. J. Symbolic Logic 20 (1955) 69-70. | Zbl 0166.27201

[11] E.F. Moore, Gedanken-experiments on sequential machines. J. Symbolic Logic 23 (1958) 60.

[12] R.E. Tarjan, Efficiency of a good but not linear set union algorithm. J. ACM 22 (1975) 215-225. | MR 458996 | Zbl 0307.68029

[13] B.W. Watson, Taxonomies and toolkit of regular languages algortihms, Ph.D. thesis. Eindhoven University of Tec. (1995). | MR 1349341 | Zbl 0832.68064

[14] B.W. Watson, An incremental DFA minimization algorithm, in International Workshop on Finite-State Methods in Natural Language Processing. Helsinki, Finland (2001).

[15] B.W. Watson and J. Daciuk, An efficient DFA minimization algorithm. Natur. Lang. Engrg. (2003) 49-64.