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.
|Title of host publication||Automata, Languages and Programming - 21st International Colloquium, ICALP 1994, Proceedings|
|Editors||Serge Abiteboul, Eli Shamir|
|Number of pages||12|
|State||Published - 1994|
|Event||Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94 - Jerusalem, Isr|
Duration: 1 Jul 1994 → 1 Jul 1994
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||Proceedings of the 1994 21st International Colloquium on Automata, Languages and Programming, ICALP'94|
|Period||1/07/94 → 1/07/94|
Bibliographical noteFunding Information:
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.
© 1994, Springer Verlag. All rights reserved.