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.