A challenging family of automata for classical minimization algorithms

Authors:
Giusi Castiglione;Cyril Nicaud;Marinella Sciortino
Affiliations:
DMI, Università di Palermo, Palermo, Italy;LIGM, Université Paris Est, Marne-la-Vallee Cedex 2, France;DMI, Università di Palermo, Palermo, Italy
Venue:
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Year:
2010

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Abstract

In this paper a particular family of deterministic automata that was built to reach the worst case complexity of Hopcroft's state minimization algorithm is considered. This family is also challenging for the two other classical minimization algorithms: it achieves the worst case for Moore's algorithm, as a consequence of a result by Berstel et al., and is of at least quadratic complexity for Brzozowski's solution, which is our main contribution. It therefore constitutes an interesting family, which can be useful to measure the efficiency of implementations of well-known or new minimization algorithms.