Journal article
On higher order homological finiteness of rewriting systems
Publication Details
Authors: | Pride, S.; Otto, F. |
Publication year: | 2005 |
Journal: | Journal of Pure and Applied Algebra |
Pages range : | 149-161 |
Volume number: | 200 |
ISSN: | 0022-4049 |
DOI-Link der Erstveröffentlichung: |
URN / URL: |
Abstract
A sequence of finite rewriting systems R-n (n >= 1) with the following properties is presented:
(1) R-n is not of type FDT,
(2) R-n is of type FHTn, but not of type FHTn+1,
(3) Rn has word problem solvable in quadratic time.
This result not only strengthens the result of Pride and Otto separating the geometric finiteness condition FDT from the finiteness condition FHT (=FHT1), but it also shows that the higher order homological finiteness conditions FHTn, which were first considered by McGlashan for dimension 2, yield an infinite hierarchy that is independent of the homotopical finiteness condition FDT. (c) 2005 Elsevier B.V. All rights reserved.
A sequence of finite rewriting systems R-n (n >= 1) with the following properties is presented:
(1) R-n is not of type FDT,
(2) R-n is of type FHTn, but not of type FHTn+1,
(3) Rn has word problem solvable in quadratic time.
This result not only strengthens the result of Pride and Otto separating the geometric finiteness condition FDT from the finiteness condition FHT (=FHT1), but it also shows that the higher order homological finiteness conditions FHTn, which were first considered by McGlashan for dimension 2, yield an infinite hierarchy that is independent of the homotopical finiteness condition FDT. (c) 2005 Elsevier B.V. All rights reserved.
