<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">J. Araújo</style></author><author><style face="normal" font="default" size="100%">Kinyon, M.</style></author><author><style face="normal" font="default" size="100%">Konieczny, J.</style></author><author><style face="normal" font="default" size="100%">Malheiro, A.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Decidability and Independence of Conjugacy Problems in Finitely Presented Monoids</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.tcs.2018.04.002</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">731</style></volume><pages><style face="normal" font="default" size="100%">88-98</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;There have been several attempts to extend the notion of conjugacy from groups to monoids.&lt;br /&gt;
The aim of this paper is study the decidability and independence of conjugacy problems&lt;br /&gt;
for three of these notions (which we will denote by $\sim_p$, $\sim_o$, and $\sim_c$) in&lt;br /&gt;
certain classes of finitely presented monoids. We will show that in the class of polycyclic monoids,&lt;br /&gt;
$p$-conjugacy is ``almost'' transitive, $\sim_c$ is strictly included in $\sim_p$, and&lt;br /&gt;
the $p$- and $c$-conjugacy problems are decidable with linear compexity.&lt;br /&gt;
For other classes of monoids, the situation is more complicated.&lt;br /&gt;
We show that there exists a monoid $M$ defined by a finite complete&lt;br /&gt;
presentation such that the $c$-conjugacy problem for $M$ is undecidable, and&lt;br /&gt;
that for finitely presented monoids, the $c$-conjugacy problem and the word&lt;br /&gt;
problem are independent, as are the  $c$-conjugacy and $p$-conjugacy problems.&lt;/p&gt;
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