PSPACE-completeness of certain algorithmic problems on the subgroups of free groups

J. C. Birget; S. Margolis; J. Meakin; P. Weil

doi:10.1007/3-540-58201-0_75

PSPACE-completeness of certain algorithmic problems on the subgroups of free groups

J. C. Birget, S. Margolis, J. Meakin, P. Weil

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

7 Scopus citations

Abstract

We investigate the solution and the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite inverse monoid Synt(H) can be canonically and effectively associated to such a subgroup H. We show that H is pure (closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this property for H is PSPACE-complete. In the process, we show that certain problems about finite automata, which are PSPACE-complete in general, remain PSPACE-complete when restricted to injective and inverse automata — whereas they are known to be in NC for permutation automata.

Original language	English
Title of host publication	Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings
Editors	Serge Abiteboul, Eli Shamir
Publisher	Springer Verlag
Pages	274-285
Number of pages	12
ISBN (Print)	9783540582014
DOIs	https://doi.org/10.1007/3-540-58201-0_75
State	Published - 1994
Externally published	Yes
Event	Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 - Jerusalem, Isr Duration: 1 Jul 1994 → 1 Jul 1994

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	820 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94
City	Jerusalem, Isr
Period	1/07/94 → 1/07/94

Bibliographical note

Publisher Copyright:
© 1994, Springer Verlag. All rights reserved.

Funding

Margolis and Meakin \[8\]f irst introduced the automata-theoretic point of view on this correspondance by showing that the finite Z-labeled graph -~H associated with * The first three authors were supported by NSF grant DMS 9203"81. The last author was partly supported by PRC Math~matiques et Informatique and by ESPRIT-BRA WG 6317 ASMICS-2. F_,-mai\]:( birget,mvxgolis)@cse.unl.edu, meakinQhoss.unl.edu, The first three authors were supported by NSF grant DMS 920381. The last author was partly supported by PRC Math?matiques et Informatique and by ESPRIT-BRAWG 6317 ASMICS-2.

Funders	Funder number
ESPRIT-BRA	WG 6317 ASMICS-2
PRC Math?matiques et Informatique	ESPRIT-BRAWG 6317 ASMICS-2
PRC Math~matiques et Informatique
National Sleep Foundation	DMS 9203"81

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10.1007/3-540-58201-0_75

Cite this

Birget, J. C., Margolis, S., Meakin, J., & Weil, P. (1994). PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. In S. Abiteboul, & E. Shamir (Eds.), Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings (pp. 274-285). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 820 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-58201-0_75

Birget, J. C. ; Margolis, S. ; Meakin, J. et al. / PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. editor / Serge Abiteboul ; Eli Shamir. Springer Verlag, 1994. pp. 274-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We investigate the solution and the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite inverse monoid Synt(H) can be canonically and effectively associated to such a subgroup H. We show that H is pure (closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this property for H is PSPACE-complete. In the process, we show that certain problems about finite automata, which are PSPACE-complete in general, remain PSPACE-complete when restricted to injective and inverse automata — whereas they are known to be in NC for permutation automata.",

author = "Birget, {J. C.} and S. Margolis and J. Meakin and P. Weil",

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Birget, JC, Margolis, S, Meakin, J & Weil, P 1994, PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. in S Abiteboul & E Shamir (eds), Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 820 LNCS, Springer Verlag, pp. 274-285, Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94, Jerusalem, Isr, 1/07/94. https://doi.org/10.1007/3-540-58201-0_75

PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. / Birget, J. C.; Margolis, S.; Meakin, J. et al.
Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. ed. / Serge Abiteboul; Eli Shamir. Springer Verlag, 1994. p. 274-285 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 820 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Birget JC, Margolis S, Meakin J, Weil P. PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. In Abiteboul S, Shamir E, editors, Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings. Springer Verlag. 1994. p. 274-285. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-58201-0_75

PSPACE-completeness of certain algorithmic problems on the subgroups of free groups

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