In computer science, Levenshtein automata are a family of finite state automata that can recognize the set V of all words in a formal language for which the Levenshtein distance to an arbitrary word W does not exceed a particular constant. A Levenshtein automaton for W can be constructed in linear time proportional to the length of W, and can identify V in much less time than would be needed if the Levenshtein distance to W was calculated for each word in the language (a problem with quadratic time complexity). Wikibooks Wikiversity has more about this subject: School of Computer Science Open Directory Project: Computer Science Downloadable Science and Computer Science books Collection of Computer Science Bibliographies Belief that title science in computer science is inappropriate Categories: | ... In the theory of computation, a finite state machine (FSM) or finite state automaton (FSA) is an abstract machine that has only a finite, constant amount of memory. ... In computer programming and some branches of mathematics, strings are sequences of various simple objects. ... In mathematics, logic and computer science, a formal language is a set of finite-length words (i. ... In information theory, the Levenshtein distance or edit distance between two strings is given by the minimum number of operations needed to transform one string into the other, where an operation is an insertion, deletion, or substitution. ... In computational complexity, an algorithm is said to take linear time, or O(n) time, if the time it requires is proportional to the size of the input, which is usually denoted n. ... Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem. ...

References

• Klaus U. Schulz, Stoyan Mihov, Fast String Correction with Levenshtein-Automata. International Journal of Document Analysis and Recognition, 5(1):67--85, 2002.