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.
The first three authors were supported by NSF grant DMS 920381. The last author was partly supported by PRC Mathématiques et Informatique and by ESPRIT-BRA WG 6317 ASMICS-2.
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© 1994 Springer-Verlag Berlin Heidelberg
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Birget, J.C., Margolis, S., Meakin, J., Weil, P. (1994). PSPACE-completeness of certain algorithmic problems on the subgroups of free groups. In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58201-0_75
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DOI: https://doi.org/10.1007/3-540-58201-0_75
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