{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article6513","name":"Efficient Minimization of DFAs with Partial Transition","abstract":"Let PT-DFA mean a deterministic finite automaton whose transition\r\n relation is a partial function. We present an algorithm for\r\n minimizing a PT-DFA in $O(m lg n)$ time and $O(m+n+alpha)$\r\n memory, where $n$ is the number of states, $m$ is the number of\r\n defined transitions, and $alpha$ is the size of the alphabet.\r\n Time consumption does not depend on $alpha$, because the $alpha$\r\n term arises from an array that is accessed at random and never\r\n initialized. It is not needed, if transitions are in a suitable\r\n order in the input. The algorithm uses two instances of an\r\n array-based data structure for maintaining a refinable partition.\r\n Its operations are all amortized constant time. One instance\r\n represents the classical blocks and the other a partition of\r\n transitions. Our measurements demonstrate the speed advantage of\r\n our algorithm on PT-DFAs over an $O(alpha n lg n)$ time,\r\n $O(alpha n)$ memory algorithm.","keywords":["Deterministic finite automaton","sparse adjacency matrix","partition refinement"],"author":[{"@type":"Person","name":"Valmari, Antti","givenName":"Antti","familyName":"Valmari"},{"@type":"Person","name":"Lehtinen, Petri","givenName":"Petri","familyName":"Lehtinen"}],"position":56,"pageStart":645,"pageEnd":656,"dateCreated":"2008-02-06","datePublished":"2008-02-06","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by-nd\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Valmari, Antti","givenName":"Antti","familyName":"Valmari"},{"@type":"Person","name":"Lehtinen, Petri","givenName":"Petri","familyName":"Lehtinen"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.STACS.2008.1328","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6204","volumeNumber":1,"name":"25th International Symposium on Theoretical Aspects of Computer Science","dateCreated":"2008-02-05","datePublished":"2008-02-05","editor":[{"@type":"Person","name":"Albers, Susanne","givenName":"Susanne","familyName":"Albers"},{"@type":"Person","name":"Weil, Pascal","givenName":"Pascal","familyName":"Weil"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article6513","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6204"}}}