Coding and information theory
Handbook of formal languages, vol. 1
Journal of Algorithms
Order-n correction for regular languages
Communications of the ACM
How hard is computing the edit distance?
Information and Computation
Handbook of Formal Languages
Handbook of Coding Theory
Descriptional complexity of error/edit systems
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the fourth international workshop on descriptional complexity of formal systems
Computing Maximal Error-detecting Capabilities and Distances of Regular Languages
Fundamenta Informaticae
The cost of traveling between languages
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Computing the edit-distance between a regular language and a context-free language
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
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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The edit distance (or Levenshtein distance) between two words is the smallest number of substitutions, insertions, and deletions of symbols that can be used to transform one of the words into the other. In this paper, we consider the problem of computing the edit distance of a regular language (the set of words accepted by a given finite automaton). This quantity is the smallest edit distance between any pair of distinct words of the language. We show that the problem is of polynomial time complexity. In particular, for a given finite automaton A with n transitions, over an alphabet of r symbols, our algorithm operates in time O(n2r2q2( q+r)), where q is either the diameter of A (if A is deterministic), or the square of the number of states in A (if A is nondeterministic). Incidentally, we also obtain an upper bound on the edit distance of a regular language in terms of the automaton accepting the language.