Efficient Minimization of DFAs with Partial Transition Functions

Antti Valmari (1) , Petri Lehtinen (1)

1 Institute of Software Systems

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.

Mots clés: deterministic finite automaton; sparse adjacency matrix; partition refinement

Domaines: Théorie de l'information [cs.IT]; Algorithme et structure de données [cs.DS]

Antti Valmari, Petri Lehtinen. Efficient Minimization of DFAs with Partial Transition Functions. STACS 2008, Feb 2008, Bordeaux, France. pp.645-656. ⟨hal-00255954⟩