Cyclic Nontrivial SCCs DFA Minimization (DFA Minimization)

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Revision as of 10:22, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Cyclic Nontrivial SCCs DFA Minimization (DFA Minimization)}} == Description == Given an finite deterministic automaton (DFA) from a class $C$ of DFAs, whose nontrivial SCCs are cyclic, determine its minimal automaton given by the equivalence relation on states. == Related Problems == Generalizations: DFA Minimization Related: Acyclic DFA Minimization == Parameters == <pre>$n$: number of states $d$: number of transitions $k$: size of alphab...")
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Description

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

Related Problems

Generalizations: DFA Minimization

Related: Acyclic 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
Almeida & Zeitoun 2008 $O(n)$ $O(n)$ Exact Deterministic Time & Space

Time Complexity graph

DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Time.png

Space Complexity graph

DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Space.png

Pareto Decades graph

DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Pareto Frontier.png