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Improved limitedness theorems on finite automata with distance functions. (English) Zbl 0693.68031

Let \({\mathcal A}\) be a finite automaton with a distance function, and ID(\({\mathcal A})\) be the set of distances associated with words accepted by \({\mathcal A}\). This paper presents an improved upper bound of ID(\({\mathcal A})\) when the upper limit of ID(\({\mathcal A})\) is finite. It also presents one necessary and sufficient condition concerning \((word,+)\)-expressions for the upper limit of ID(\({\mathcal A})\) to be infinite.

MSC:

68Q45 Formal languages and automata
68Q25 Analysis of algorithms and problem complexity
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