Decidability and independence of conjugacy problems in finitely presented monoids

João Araújo, Michael Kinyon, Janusz Konieczny, António Malheiro

Research output: Contribution to journalArticle

Abstract

There have been several attempts to extend the notion of conjugacy from groups to monoids. The aim of this paper is study the decidability and independence of conjugacy problems for three of these notions (which we will denote by ∼p, ∼o, and ∼c) in certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids, p-conjugacy is “almost” transitive, ∼c is strictly included in ∼p, and the p- and c-conjugacy problems are decidable with linear complexity on a two-tape Turing Machine. For other classes of monoids, the situation is more complicated. We show that there exists a monoid M defined by a finite complete presentation such that the c-conjugacy problem for M is undecidable, and that for finitely presented monoids, the c-conjugacy problem and the word problem are independent, as are the c-conjugacy and p-conjugacy problems. On other hand, we show that for finitely presented monoids, the o-conjugacy problem is reducible to the c-conjugacy problem.

Original languageEnglish
Pages (from-to)88-98
Number of pages11
JournalTheoretical Computer Science
Volume731
DOIs
Publication statusPublished - 30 Jun 2018

Keywords

  • Complexity
  • Conjugacy
  • Decidability
  • Decision problem
  • Finitely presented monoids
  • Independence
  • Polycyclic monoids

Fingerprint Dive into the research topics of 'Decidability and independence of conjugacy problems in finitely presented monoids'. Together they form a unique fingerprint.

Cite this