DFA Minimization (DFA Minimization)
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Description
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
Parameters
$n$: 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
Space Complexity Graph
Space-Time Tradeoff Improvements
