Short Regular Expressions from Finite Automata: Empirical Results
We continue our work [H. Gruber, M. Holzer: Provably shorter regular expressions from deterministic finite automata (extended abstract). In Proc. DLT, LNCS 5257, 2008] on the problem of finding good elimination orderings for the state elimination algorithm, one of the most popular algorithms for the conversion of finite automata into equivalent regular expressions. Here we tackle this problem both from the theoretical and from the practical side. First we show that the problem of finding optimal elimination orderings can be used to estimate the cycle rank of the underlying automata. This gives good evidence that the problem under consideration is difficult, to a certain extent. Moreover, we conduct experiments on a large set of carefully chosen instances for five different strategies to choose elimination orderings, which are known from the literature. Perhaps the most surprising result is that a simple greedy heuristic by [M. Delgado, J. Morais: Approximation to the smallest regular expression for a given regular language. In Proc. CIAA, LNCS 3317, 2004] almost always outperforms all other strategies, including those with a provable performance guarantee.
KeywordsRegular Expression Regular Language Finite Automaton Elimination Ordering Input Alphabet
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- 9.Gelade, W., Neven, F.: Succinctness of the complement and intersection of regular expressions. In: STACS 2008. Dagstuhl Seminar Proceedings, vol. 08001, pp. 325–336. IBFI Schloss Dagstuhl (2008)Google Scholar
- 15.Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Automata studies, pp. 3–42. Princeton University Press, Princeton (1956)Google Scholar
- 17.Morgan, K.: Approximation algorithms for the maximum induced planar and outerplanar subgraph problems. Bachelor with honors thesis, Monash University, Australia (2005)Google Scholar