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

University of Nebraska-Lincoln
Université Paris 6

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

8 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

Access to Document

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)).

@inproceedings{b8a05262866e465386c430cfe75d9a5e,

title = "PSPACE-completeness of certain algorithmic problems on the subgroups of free groups",

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",

note = "Publisher Copyright: {\textcopyright} 1994, Springer Verlag. All rights reserved.; Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 ; Conference date: 01-07-1994 Through 01-07-1994",

year = "1994",

doi = "10.1007/3-540-58201-0\_75",

language = "אנגלית",

isbn = "9783540582014",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "274--285",

editor = "Serge Abiteboul and Eli Shamir",

booktitle = "Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings",

address = "גרמניה",

}

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

TY - GEN

T1 - PSPACE-completeness of certain algorithmic problems on the subgroups of free groups

AU - Birget, J. C.

AU - Margolis, S.

AU - Meakin, J.

AU - Weil, P.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0039585660

U2 - 10.1007/3-540-58201-0_75

DO - 10.1007/3-540-58201-0_75

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:0039585660

SN - 9783540582014

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 274

EP - 285

BT - Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings

A2 - Abiteboul, Serge

A2 - Shamir, Eli

PB - Springer Verlag

T2 - Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94

Y2 - 1 July 1994 through 1 July 1994

ER -

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

Abstract

Publication series

Conference

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this