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Incremental construction and maintenance of minimal finite-state automata. (English) Zbl 1232.68080
Summary: J. Daciuk et al. [ibid. 26, No. 1, 3–16 (2000; Zbl 1232.68081)] describe a method for constructing incrementally minimal, deterministic, acyclic finite-state automata (dictionaries) from sets of strings. But acyclic finite-state automata have limitations: For instance, if one wants a linguistic application to accept all possible integer numbers or Internet addresses, the corresponding finite state automaton has to be cyclic. In this article, we describe a simple and equally efficient method for modifying any minimal finite-state automaton (be it acyclic or not) so that a string is added to or removed from the language it accepts; both operations are very important when dictionary maintenance is performed and solve the dictionary construction problem addressed in [loc. cit.] as a special case. The algorithms proposed here may be straightforwardly derived from the customary textbook constructions for the intersection and the complementation of finite-state automata; the algorithms exploit the special properties of the automata resulting from the intersection operation when one of the finite-state automata accepts a single string.

MSC:
68Q45 Formal languages and automata
91F20 Linguistics
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[1] DOI: 10.1162/089120100561601 · Zbl 1232.68081 · doi:10.1162/089120100561601
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