Efficient Minimization of DFAs with Partial Transition
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.
Deterministic finite automaton
sparse adjacency matrix
partition refinement
645-656
Regular Paper
Antti
Valmari
Antti Valmari
Petri
Lehtinen
Petri Lehtinen
10.4230/LIPIcs.STACS.2008.1328
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