An assessment of algorithms for deriving failure deterministic finite automata

Nxumalo, Madoda ; Kourie, Derrick G. ; Cleophas, Loek ; Watson, Bruce W. (2017)

CITATION: Nxumalo, M., et al. 2017. An assessment of algorithms for deriving failure deterministic finite automata. South African Computer Journal, 29(1):43-68, doi:10.18489/sacj.v29i1.456.

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Failure deterministic finite automata (FDFAs) represent regular languages more compactly than deterministic finite automata (DFAs). Four algorithms that convert arbitrary DFAs to language-equivalent FDFAs are empirically investigated. Three are concrete variants of a previously published abstract algorithm, the DFA-Homomorphic Algorithm (DHA). The fourth builds a maximal spanning tree from the DFA to derive what it calls a delayed input DFA. A first suite of test data consists of DFAs that recognise randomised sets of finite length keywords. Since the classical Aho-Corasick algorithm builds an optimal FDFA from such a set (and only from such a set), it provides benchmark FDFAs against which the performance of the general algorithms can be compared. A second suite of test data consists of random DFAs generated by a specially designed algorithm that also builds language-equivalent FDFAs, some of which may have non-divergent cycles. These random FDFAs provide (not necessarily tight) lower bounds for assessing the effectiveness of the four general FDFA generating algorithms.

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