Cyclic Nontrivial SCCs DFA Minimization: Difference between revisions

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== Time Complexity graph ==  
== Time Complexity Graph ==  


[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Time.png|1000px]]
[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Time.png|1000px]]


== Space Complexity graph ==  
== Space Complexity Graph ==  


[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Space.png|1000px]]
[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Space.png|1000px]]


== Pareto Decades graph ==  
== Pareto Frontier Improvements Graph ==  


[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Pareto Frontier.png|1000px]]
[[File:DFA Minimization - Cyclic Nontrivial SCCs DFA Minimization - Pareto Frontier.png|1000px]]

Revision as of 13:04, 15 February 2023

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 Frontier Improvements Graph

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