Rational equivalence relations
Theoretical Computer Science
Improved limitedness theorems on finite automata with distance functions
Theoretical Computer Science - Special issue on theoretical computer science, algebra and combinatorics
Synchronized rational relations of finite and infinite words
Theoretical Computer Science - Selected papers of the International Colloquium on Words, Languages and Combinatorics, Kyoto, Japan, August 1990
Automata, Languages, and Machines
Automata, Languages, and Machines
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Computing Maximal Error-detecting Capabilities and Distances of Regular Languages
Fundamenta Informaticae
Bounded repairability of word languages
Journal of Computer and System Sciences
Approximate matching between a context-free grammar and a finite-state automaton
CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata
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We extend the Hamming, edit, prefix, suffix and subword distances between strings to subsets of strings. We show that computing these distances between two rational subsets reduces to computing the weight of an automaton "with distance function" as introduced by Hashiguchi (this latter notion of distance has nothing to do with our notion). We make a step further by extending the notion of distance between subsets to that of "almost reflexivity" of relations over strings: intuitively a relation is almost reflexive if every element of its domain is in relation with some "close" element in its range and vice versa. Various properties connected to almost reflexivity are investigated. With two exceptions, their decidability status relative to the five notions of distances is settled for the three families of recognizable, synchronous and deterministic relations.