Iain A. Stewart, Refining known results on the generalized word problem for free groups. International Journal of Algebra and Computation 2(2) (1992), 221--236. Home/Search Document Not in Database Summary Related Articles Check |
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PSPACE-complete problems for subgroups of free groups .. - Birget, Margolis.. (2000) (1 citation) (Correct)
....in its infancy . Regarding finitely generated subgroups of free groups, it is known that the generalized word problem and the conjugacy problem can be solved in polynomial time. These problems are in fact complete for P via logspace reductions (Avenhaus and Madlener, 1] 2] for refinements, see [25]) Thus the problem of deciding purity is one of the few provably hard decidable problems known (as of today) in combinatorial group theory. 1 Inverse automata First we fix some notation. Let # be an alphabet, i.e. a finite set, and let # # be the free monoid on #, that is, the set of all words ....
I.A. Stewart, "Refining known results on the generalized word problem for free groups", International J. Algebra and Computation 2 (1992) 221-236.
A Compendium of Problems Complete for Symmetric Logarithmic.. - Alvarez, Greenlaw (1996) (7 citations) (Correct)
....GWPC(2) is in SL. For the completeness proof see [26, Corollary on page 267] Remarks: GWPC(2) is called the Generalized Word Problem for finitelygenerated subgroups of Countably generated free groups with generators of length 2 in [26] For general k certain variants of the problem are Pcomplete [27]. See Stewart [26, 27] for additional details and definitions. 8 Open Problems In this section we list a number of open problems. For each problem we provide a definition, remarks, and a reference. 1 The goal in each case is to show that the problem is SL hard under m log reducibility. In ....
.... For the completeness proof see [26, Corollary on page 267] Remarks: GWPC(2) is called the Generalized Word Problem for finitelygenerated subgroups of Countably generated free groups with generators of length 2 in [26] For general k certain variants of the problem are Pcomplete [27] See Stewart [26, 27] for additional details and definitions. 8 Open Problems In this section we list a number of open problems. For each problem we provide a definition, remarks, and a reference. 1 The goal in each case is to show that the problem is SL hard under m log reducibility. In some cases the problem ....
Iain A. Stewart. Refining known results on the generalized word problem for free groups. International Journal of Algebra and Computation, 2(2):221--236, June 1992.
A Compendium of Problems Complete for Symmetric Logarithmic.. - Alvarez, Greenlaw (1996) (7 citations) (Correct)
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Iain A. Stewart, Refining known results on the generalized word problem for free groups. International Journal of Algebra and Computation 2(2) (1992), 221--236.
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