DFA Minimization: Difference between revisions
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== Parameters == | == Parameters == | ||
$n$: number of states | |||
$d$: number of transitions | $d$: number of transitions | ||
$k$: size of alphabet | |||
$k$: size of alphabet | |||
== Table of Algorithms == | == Table of Algorithms == | ||
| Line 29: | Line 31: | ||
|- | |- | ||
| [[Brzozowski's algorithm (DFA Minimization DFA Minimization)|Brzozowski's algorithm]] || 1963 || $O({2}^n)$ || $O({2}^n)$ || Exact || Deterministic || [https://www.semanticscholar.org/paper/Canonical-regular-expressions-and-minimal-state-for-Brzozowski/94def4233e1e8f15bab72e82708a03fd37233b14 Time] & [http://www.cs.ru.nl/bachelors-theses/2017/Erin_van_der_Veen___4431200___The_Practical_Performance_of_Automata_Minimization_Algorithms.pdf Space] | | [[Brzozowski's algorithm (DFA Minimization DFA Minimization)|Brzozowski's algorithm]] || 1963 || $O({2}^n)$ || $O({2}^n)$ || Exact || Deterministic || [https://www.semanticscholar.org/paper/Canonical-regular-expressions-and-minimal-state-for-Brzozowski/94def4233e1e8f15bab72e82708a03fd37233b14 Time] & [http://www.cs.ru.nl/bachelors-theses/2017/Erin_van_der_Veen___4431200___The_Practical_Performance_of_Automata_Minimization_Algorithms.pdf Space] | ||
|- | |||
| [[Revuz's algorithm (Acyclic DFA Minimization DFA Minimization)|Revuz's algorithm]] || 1992 || $O(n)$ || $O(n)$ || Exact || Deterministic || [https://www.sciencedirect.com/science/article/pii/0304397592901423 Time] & [https://www.labri.fr/perso/zeitoun/research/pdf/Almeida-Zeitoun-IPL2008.pdf Space] | |||
|- | |||
| [[Almeida & Zeitoun (Cyclic Nontrivial SCCs DFA Minimization DFA Minimization)|Almeida & Zeitoun]] || 2008 || $O(n)$ || $O(n)$ || Exact || Deterministic || [https://www.labri.fr/perso/zeitoun/research/pdf/Almeida-Zeitoun-IPL2008.pdf Time & Space] | |||
|- | |- | ||
|} | |} | ||
== Time Complexity | == Time Complexity Graph == | ||
[[File:DFA Minimization - Time.png|1000px]] | [[File:DFA Minimization - Time.png|1000px]] | ||
Latest revision as of 09:08, 28 April 2023
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
