Complexity of a Problem Concerning Reset Words for Eulerian Binary Automata
Vojt\v{e}ch Vorel
TL;DR
This paper proves that determining the existence of a reset word within a maximum length remains NP-complete even for Eulerian automata with binary alphabets, confirming a conjecture by Martyugin.
Contribution
It establishes the NP-completeness of the reset word problem for Eulerian binary automata, extending the known complexity results to this specific class.
Findings
NP-complete problem persists for Eulerian binary automata
Confirms Martyugin's conjecture from 2011
Extends complexity results to a restricted automaton class
Abstract
A word is called a reset word for a deterministic finite automaton if it maps all the states of the automaton to a unique state. Deciding about the existence of a reset word of a given maximum length for a given automaton is known to be an NP-complete problem. We prove that it remains NP-complete even if restricted to Eulerian automata with binary alphabets, as it has been conjectured by Martyugin (2011).
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Taxonomy
Topicssemigroups and automata theory · DNA and Biological Computing · Algorithms and Data Compression