eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-07-04
139:1
139:14
10.4230/LIPIcs.ICALP.2018.139
article
The Isomorphism Problem for Finite Extensions of Free Groups Is In PSPACE
Sénizergues, Géraud
1
Weiß, Armin
2
LABRI, Bordeaux, France
Universität Stuttgart, FMI, Germany
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol107-icalp2018/LIPIcs.ICALP.2018.139/LIPIcs.ICALP.2018.139.pdf
virtually free groups
context-free groups
isomorphism problem
structure tree
graph of groups