## 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

### Keywords:

finite automaton; distance function; upper bound
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### References:

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