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Efficient Minimization of DFAs with Partial Transition Valmari, Antti Lehtinen, Petri Deterministic finite automaton sparse adjacency matrix partition refinement Let PT-DFA mean a deterministic finite automaton whose transition relation is a partial function. We present an algorithm for minimizing a PT-DFA in $O(m lg n)$ time and $O(m+n+alpha)$ memory, where $n$ is the number of states, $m$ is the number of defined transitions, and $alpha$ is the size of the alphabet. Time consumption does not depend on $alpha$, because the $alpha$ term arises from an array that is accessed at random and never initialized. It is not needed, if transitions are in a suitable order in the input. The algorithm uses two instances of an array-based data structure for maintaining a refinable partition. Its operations are all amortized constant time. One instance represents the classical blocks and the other a partition of transitions. Our measurements demonstrate the speed advantage of our algorithm on PT-DFAs over an $O(alpha n lg n)$ time, $O(alpha n)$ memory algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Antti Valmari and Petri Lehtinen 2008 Is Part Of LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2008.1328 urn:nbn:de:0030-drops-13286 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1328 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode