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Inverse automata andmonoids and the undecidability of the cayley subgraph problem for groups

Published online by Cambridge University Press:  08 November 2000

Ana Oliveira  and
Pedro V. Silva
Ana Oliveira
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, 4099-002 Porto, Portugal website: http://www.fc.up.pt/cmup
Pedro V. Silva
Affiliation:
Centro de Matemática, Faculdade de Ciências, Universidade do Porto, 4099-002 Porto, Portugal website: http://www.fc.up.pt/cmup
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Abstract

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The structure of an inverse monoid can bedetermined by the complete set of Schützenberger graphs of a presentation. Necessary andsufficient conditions for a collection of inverse X-graphs to be the complete set ofSchützenberger graphs of some inverse monoid presentation are established and decidabilityresults are obtained. Conditions for a single inverse X-graph to be a Schu¨tzenbergergraph for some presentation are also obtained, and both problems are restricted to the case ofClifford monoids and E-unitary inverse monoids. Decidability and undecidability results are obtainedfor the case of finite graphs. It is also proved that the problem of embedding a finite inverseX-graph in the Cayley graph of a group is undecidable.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 3 , September 2000 , pp. 421 - 437
Copyright
2000 Glasgow Mathematical Journal Trust