Abstract
We give an algorithm producing from every p.d.a. M recognizing the word-problem for an infinite group G, a decomposition of G as an amalgamated product (with finite amalgamated subgroups) or as an HNN-extension (with finite associated subgroups).This algorithm has an elementary time-complexity.This result allows us to show that the isomorphism-problem for finitely generated virtually-free groups is primitive recursive, thus improving the decidability result of [Krstic,1989].
This work has been supported by the ESPRIT Basic Research Working Group “COMPUGRAPH II” and by the PRC MathInfo
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
A. V. Anisimov. Group languages. Kibernetica 4, pages 18–24, 1971.
J.M. Autebert, L. Boasson, and G. Sénizergues. Groups and nts languages. JCSS vol.35, no2, pages 243–267, 1987.
L. Boasson and M. Nivat. Centers of context-free languages. LITP technical report no84-44, 1984.
J.R. Buchi. Regular canonical systems, the collected works of J.R. Buchi, 1990.
D.E. Cohen. Groups of cohomological dimension one. Lectures Notes in math.,Springer vol.245, 1972.
B. Courcelle. The monadic second-order logic of graphs ii: infinite graphs of bounded width. Math. Systems Theory 21, pages 187–221, 1990.
W. Dicks and M.J. Dunwoody. Groups acting on graphs. Cambridge University Press, 1990.
D.B.A. Epstein, J.W. Cannon, D.F. Holt, S.V.F. Levy, M.S. Paterson, and W.P. Thurston. Word processing in groups. Jones and Bartlett, 1992.
S. Krstic. Actions of finite groups on graphs and related automorphisms of free groups. Journal of algebra 124, pages 119–138, 1989.
D.E. Muller and P.E. Schupp. Groups, the theory of ends and context-free languages. JCSS vol 26, no 3, pages 295–310, 1983.
D.E. Muller and P.E. Schupp. The theory of ends, pushdown automata and second-order logic. TCS 37, pages 51–75, 1985.
J. Sakarovitch. Description des monodes de type fini. Elektronische Informationsverarbeitung und Kybernetic 17, pages 417–434, 1981.
G. Sénizergues. On the finite subgroups of a context-free group, in preparation, 199?
Stallings. On torsion-free groups with infinitely many ends. Ann. of Math. 88, pages 312–334, 1968.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sénizergues, G. (1993). An effective version of Stallings' theorem in the case of context-free groups. In: Lingas, A., Karlsson, R., Carlsson, S. (eds) Automata, Languages and Programming. ICALP 1993. Lecture Notes in Computer Science, vol 700. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56939-1_96
Download citation
DOI: https://doi.org/10.1007/3-540-56939-1_96
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56939-8
Online ISBN: 978-3-540-47826-3
eBook Packages: Springer Book Archive