Approximate Membership for Regular Languages modulo the Edit Distance

International audienceWe present a probabilistic algorithm for testing approximate membership of words to regular languages modulo the edit distance. The time complexity of our algorithm, which is independent of the size of the input word, is polynomial in the size of the input automaton and the inverse error precision. All previous property testing algorithms for regular languages, whether they consider approximations modulo the Hamming distance or the edit distance with moves, run in exponential time if not fixing one of these parameters