PSPACE-complete problems for subgroups of free groups and inverse finite automata

Theoretical Computer Science

Volumn 242, Issue 1-2, 2000, Pages 247-281

  Birget, J C ^a   Margolis, S ^b   Meakin, J ^a   Weil, P ^c  

^a UNIVERSITY OF NEBRASKA LINCOLN   (United States)

^b BAR ILAN UNIVERSITY   (Israel)

^c UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Inverse automata; PSPACE completeness; Pure subgroups; Subgroups of the free group

Indexed keywords

EID: 0001406323     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00225-4     Document Type: Article

References (27)

1. J. Avenhaus, K. Madlener, The Nielsen reduction and P-complete problems in free groups, Theoret. Comput. Sci. 32 (1984) 61-76.
2. J. Avenhaus, K. Madlener, On the complexity of intersection and conjugacy problems in free groups, Theoret. Comput. Sci. 32 (1984) 279-295.
3. L. Babai, E. Luks, A. Seress, Permutation groups in NC, Proc. 19th ACM Annual Symp. on Theory of Computing, 1987, pp. 409-420.
4. C. Bennett, Time/Space tradeoffs for reversible computation, SIAM J. Comput. 18 (1989) 766-776.
5. J. Berstel, Transductions and Context-Free Languages, Teubner, Stuttgart, 1979.
6. S. Cho, D. Huynh, Finite-automaton aperiodicity is PSPACE-complete, Theoret. Comput. Sci. 88 (1991) 99-116.
7. D.E. Cohen, Combinatorial Group Theory: A Topological Approach, London Math. Soc. Student Texts 14, Cambridge University Press, Cambridge, 1989.
8. D. Cowan, Inverse monoids of dot-depth two, Internat. J. Algebra Comput. 3 (1993) 411-424.
9. S. Eilenberg, Automata, Languages and Machines, vol. B, Academic Press, New York, 1976.
10. M. Garey, D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
11. J. Hopcroft, J. Ullman, Introduction to Automata Theory, Formal Languages and Computation, Addison-Wesley, Reading, MA, 1979.
12. D. Kozen, Lower bounds for natural proof systems, Proc. 18th IEEE Annual Symp. on Foundations of Computer Science, 1977, pp. 254-266.
13. R. Levine, A. Sherman, A note on Bennett's time-space tradeoff for reversible computations, SIAM J. Comput. 19 (1990) 673-677.
14. R. Lyndon, P. Schupp, Combinatorial Group Theory, Springer, New York, 1977.
15. S. Margolis, J. Meakin, Free inverse monoids and graph immersions, Internat. J. Algebra Comput. 3 (1993) 79-100.
16. R. McNaughton, S. Papert, Counter-free Automata, MIT Press, New York, 1971.
17. M. Petrich, Inverse Monoids, Wiley, New York, 1984.
18. J.-E. Pin, Variétés de langages formels, Masson, Paris, 1984. English translation: Varieties of formal languages, North Oxford, London, 1986.
19. J.-E. Pin, Variétés de langages formels, Masson, Paris, 1984. English translation: Varieties of formal languages, North Oxford, London, 1986.
20. K. Reidemeister, Fundamentalgruppen und Überlagerungsräume, Nachrichten der Ges. Wiss., Math. Phys. Klasse Göttingen, 1928, pp. 69-76.
21. R. Ruyle, Pseudovarieties of inverse monoids Ph.D. Dissertation, University of Nebraska-Lincoln, 1997.
22. J. Sakarovitch, A problem on rational subsets of the free group, Amer. Math. Monthly 91 (1984) 499-501.
23. C. Sims, Computation with Finitely Presented Groups, Cambridge, London, 1995.
24. J. Stallings, The topology of graphs, Invent. Math. 71 (1983) 551-565.
25. J. Stern, Complexity of some problems from the theory of automata, Inform, and Control 66 (1985) 163-176.
26. I.A. Stewart, Refining known results on the generalized word problem for free groups, Internat. J. Algebra Comput. 2 (1992) 221-236.
27. P. Weil, Inverse monoids and the dot-depth hierarchy, Ph.D. Dissertation, University of Nebraska-Lincoln, 1988.