Abstract
We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and effectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this property of 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 (with single accept state), whereas they are known to be in NC for permutation automata (with single accept state).
| Original language | English |
|---|---|
| Pages (from-to) | 247-281 |
| Number of pages | 35 |
| Journal | Theoretical Computer Science |
| Volume | 242 |
| Issue number | 1-2 |
| DOIs | |
| State | Published - 6 Jul 2000 |
Bibliographical note
Funding Information:∗Corresponding author. E-mail address: [email protected] (P. Weil). 1The rst three authors were supported by NSF Grant 92-03981. The fourth author was supported by GdR-PRC AMI. All four authors were supported by the Center for Communication and Information Sciences, University of Nebraska-Lincoln.
Funding
∗Corresponding author. E-mail address: [email protected] (P. Weil). 1The rst three authors were supported by NSF Grant 92-03981. The fourth author was supported by GdR-PRC AMI. All four authors were supported by the Center for Communication and Information Sciences, University of Nebraska-Lincoln.
| Funders | Funder number |
|---|---|
| Center for Communication and Information Sciences, University of Nebraska-Lincoln | |
| GdR-PRC AMI | |
| National Science Foundation | 92-03981 |
Keywords
- Inverse automata
- PSPACE-completeness
- Pure subgroups
- Subgroups of the free group