Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.139
URN: urn:nbn:de:0030-drops-91437
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9143/
Sénizergues, Géraud ; Weiß, Armin
The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE
| pdf-format: |
|
Abstract
We present an algorithm for the following problem: given a context-free grammar for the word problem of a virtually free group G, compute a finite graph of groups G with finite vertex groups and fundamental group G. Our algorithm is non-deterministic and runs in doubly exponential time. It follows that the isomorphism problem of context-free groups can be solved in doubly exponential space. Moreover, if, instead of a grammar, a finite extension of a free group is given as input, the construction of the graph of groups is in NP and, consequently, the isomorphism problem in PSPACE.
BibTeX - Entry
@InProceedings{snizergues_et_al:LIPIcs:2018:9143,
author = {G{\'e}raud S{\'e}nizergues and Armin Wei{\ss}},
title = {{The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE}},
booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
pages = {139:1--139:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-076-7},
ISSN = {1868-8969},
year = {2018},
volume = {107},
editor = {Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9143},
URN = {urn:nbn:de:0030-drops-91437},
doi = {10.4230/LIPIcs.ICALP.2018.139},
annote = {Keywords: virtually free groups, context-free groups, isomorphism problem, structure tree, graph of groups}
}
| Keywords: | virtually free groups, context-free groups, isomorphism problem, structure tree, graph of groups | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
