{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article1947","name":"Application of verification techniques to inverse monoids","abstract":"The word problem for inverse monoids generated by\r\na set $Gamma$ subject to relations of the form $e=f$, where $e$ and $f$\r\nare both idempotents in the free inverse monoid generated by $Gamma$,\r\nis investigated. It is\r\nshown that for every fixed monoid of this form the word problem\r\ncan be solved in polynomial time which solves an open problem of\r\nMargolis and Meakin. For the uniform word problem, where the presentation is\r\npart of the input, EXPTIME-completeness is shown.\r\nFor the Cayley-graphs of these\r\nmonoids, it is shown that the first-order theory with regular path\r\npredicates is decidable. Regular path predicates allow to state\r\nthat there is a path from a node $x$ to a node $y$ that is labeled\r\nwith a word from some regular language. As a corollary, the decidability\r\nof the generalized word problem is deduced. Finally, some results\r\non free partially commutative inverse monoids are presented.","keywords":["Inverse monoids","word problems","Cayley-graphs","complexity"],"author":{"@type":"Person","name":"Lohrey, Markus","givenName":"Markus","familyName":"Lohrey"},"position":3,"pageStart":1,"pageEnd":15,"dateCreated":"2008-04-09","datePublished":"2008-04-09","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Lohrey, Markus","givenName":"Markus","familyName":"Lohrey"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.07441.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume672","volumeNumber":7441,"name":"Dagstuhl Seminar Proceedings, Volume 7441","dateCreated":"2008-04-09","datePublished":"2008-04-09","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article1947","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume672"}}}