Better hyper-minimization: not as fast, but fewer errors

Authors:
Andreas Maletti
Affiliations:
Departament de Filologies Romàniques, Universitat Rovira i Virgili, Tarragona, Spain
Venue:
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
Year:
2010

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Abstract

Hyper-minimization aims to compute a minimal deterministic finite automaton (DFA) that recognizes the same language as a given DFA up to a finite number of errors. Algorithms for hyper-minimization that run in time O(n log n), where n is the number of states of the given DFA, have been reported recently in [GAWRYCHOWSKI and JEŻ: Hyperminimisation made efficient. Proc. MFCS, LNCS 5734, 2009] and [HOLZER and MALETTI: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. These algorithms are improved to return a hyper-minimal dfa that commits the least number of errors. This closes another open problem of [BADR, GEFFERT, and SHIPMAN: Hyper-minimizing minimized deterministic finite state automata. RAIRO Theor. Inf. Appl. 43, 2009]. Unfortunately, the time complexity for the obtained algorithm increases to O(n2).