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http://dx.doi.org/10.18419/opus-11768
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DC Field | Value | Language |
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dc.contributor.author | Stober, Florian | - |
dc.date.accessioned | 2021-11-04T13:27:26Z | - |
dc.date.available | 2021-11-04T13:27:26Z | - |
dc.date.issued | 2021 | de |
dc.identifier.other | 177644132X | - |
dc.identifier.uri | http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-117857 | de |
dc.identifier.uri | http://elib.uni-stuttgart.de/handle/11682/11785 | - |
dc.identifier.uri | http://dx.doi.org/10.18419/opus-11768 | - |
dc.description.abstract | This thesis studies the complexity of the power word problem in graph groups. The power word problem is a variant of the word problem, where the input is a power word. A power word is a compact representation of a word. It may contain powers p^x, where p is a finite word and x is a binary encoded integer. A graph group, also known as right-angled Artin group or partially commutative group is a free group augmented with commutation relations. We show that the power word problem in graph groups can be decided in polynomial time, and more precisely it is AC^0-Turing-reducible to the word problem of the free group with two generators F_2. Being a generalization of graph groups, we also look into the power word problem in graph products. The power word problem in a fixed graph product is AC^0-Turing-reducible to the word problem of the free group F_2 and the power word problem of the base groups. Furthermore, we look into the uniform power word problem in a graph product, where the dependence graph and the base groups are part of the input. Given a class of finitely generated groups C, the uniform power word problem in a graph product is CL-Turing-reducible to the word problem in the free group F_2 and the uniform power word problem in C. Finally, we show that as a consequence of our results on the power word problem the uniform knapsack problem in graph groups is NP-complete. | en |
dc.language.iso | en | de |
dc.rights | info:eu-repo/semantics/openAccess | de |
dc.subject.ddc | 004 | de |
dc.title | The power word problem in graph groups | en |
dc.type | masterThesis | de |
ubs.fakultaet | Informatik, Elektrotechnik und Informationstechnik | de |
ubs.institut | Institut für Formale Methoden der Informatik | de |
ubs.publikation.seiten | 65 | de |
ubs.publikation.typ | Abschlussarbeit (Master) | de |
Appears in Collections: | 05 Fakultät Informatik, Elektrotechnik und Informationstechnik |
Files in This Item:
File | Description | Size | Format | |
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MasterThesis_FlorianStober.pdf | 850,5 kB | Adobe PDF | View/Open |
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