From Nerode’s congruence to suffix automata with mismatches |
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Authors: | M Crochemore C Epifanio A Gabriele F Mignosi |
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Affiliation: | 1. King’s College London, UK;2. Institut Gaspard-Monge, Université Paris-Est, France;3. Dipartimento di Matematica e Applicazioni, Università di Palermo, Italy;4. Dipartimento di Informatica, Università dell’Aquila, Italy |
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Abstract: | In this paper we focus on the minimal deterministic finite automaton Sk that recognizes the set of suffixes of a word w up to k errors. As first result we give a characterization of the Nerode’s right-invariant congruence that is associated with Sk. This result generalizes the classical characterization described in A. Blumer, J. Blumer, D. Haussler, A. Ehrenfeucht, M. Chen, J. Seiferas, The smallest automaton recognizing the subwords of a text, Theoretical Computer Science, 40, 1985, 31–55]. As second result we present an algorithm that makes use of Sk to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text, where r is the repetition index of w. Moreover, we give some experimental results on some well-known words, like prefixes of Fibonacci and Thue-Morse words. Finally, we state a conjecture and an open problem on the size and the construction of the suffix automaton with mismatches. |
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Keywords: | Combinatorics on words Indexing Suffix automata Languages with mismatches Approximate string matching |
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