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http://dx.doi.org/10.18419/opus-2548
Autor(en): | Lohrey, Markus Ondrusch, Nicole |
Titel: | Inverse monoids : decidability and complexity of algebraic questions |
Erscheinungsdatum: | 2005 |
Dokumentart: | Arbeitspapier |
Serie/Report Nr.: | Technischer Bericht / Universität Stuttgart, Fakultät Informatik, Elektrotechnik und Informationstechnik;2005,2 |
URI: | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-22557 http://elib.uni-stuttgart.de/handle/11682/2565 http://dx.doi.org/10.18419/opus-2548 |
Zusammenfassung: | This paper investigates the word problem for inverse monoids generated by a set A subject to relations of the form e=f, where e and f are both idempotents in the free inverse monoid generated by A. It is shown that for every fixed monoid of this form the word problem can be solved in polynomial time which solves an open problem of Margolis and Meakin. For the uniform word problem, where the presentation is part of the input, EXPTIME-completeness is shown. For the Cayley-graphs of these monoids, it is shown that the first-order theory with regular path predicates is decidable. Regular path predicates allow to state that there is a path from a node x to a node y that is labeled with a word from some regular language. As a corollary, the decidability of the generalized word problem is deduced. Finally, it is shown that the Cayley-graph of the free inverse monoid has an undecidable monadic second-order theory. |
Enthalten in den Sammlungen: | 05 Fakultät Informatik, Elektrotechnik und Informationstechnik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
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TR_2005_02.pdf | 225,9 kB | Adobe PDF | Öffnen/Anzeigen |
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