DFA Minimization (DFA Minimization)

From Algorithm Wiki
Jump to navigation Jump to search


Given a finite deterministic automaton (DFA) from a class $C$ of DFAs, determine its minimal automaton given by the equivalence relation on states.

Related Problems

Subproblem: Acyclic DFA Minimization, Cyclic Nontrivial SCCs DFA Minimization

Related: Cyclic Nontrivial SCCs DFA Minimization


$n$: number of states

$d$: number of transitions

$k$: size of alphabet

Table of Algorithms

Name Year Time Space Approximation Factor Model Reference
Hopcroft's algorithm 1971 $O(kn \log n)$ $O(kn)$ Exact Deterministic Time & Space
Moore's algorithm 1956 $O(n^{2} k)$ $O(n)$ Exact Deterministic Time
Brzozowski's algorithm 1963 $O({2}^n)$ $O({2}^n)$ Exact Deterministic Time & Space
Revuz's algorithm 1992 $O(n)$ $O(n)$ Exact Deterministic Time & Space
Almeida & Zeitoun 2008 $O(n)$ $O(n)$ Exact Deterministic Time & Space

Time Complexity Graph

DFA Minimization - Time.png