The neighbourhood of a language [Formula: see text] with respect to an additive distance consists of all strings that have distance at most the given radius from some string of [Formula: see text]. We show that the worst case deterministic state complexity of a radius [Formula: see text] neighbourhood of a language recognized by an [Formula: see text] state nondeterministic finite automaton [Formula: see text] is [Formula: see text]. In the case where [Formula: see text] is deterministic we get the same lower bound for the state complexity of the neighbourhood if we use an additive quasi-distance. The lower bound constructions use an alphabet of size linear in [Formula: see text]. We show that the worst case state complexity of the set of strings that contain a substring within distance [Formula: see text] from a string recognized by [Formula: see text] is [Formula: see text].
We generalize a theorem due to Keilson on the approximate exponentiality of waiting times for rare events in regenerative processes. We use the result to investigate the limit distribution for a family of first entrance times in a sequence of Ehrenfest urn models. As a second application, we consider approximate pattern matching, a problem arising in molecular biology and other areas.
Computing quality scores and uncertainty for approximate pattern matching in geospatial semantic graphs
