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Ivanov, Sergei V. Kapovitch, Ilia Ivanov, Sergei V. Leininger, Christopher J. Schupp, Paul E. Cummins, Desmond 2012-09-18T21:18:24Z 2012-09-18T21:18:24Z 2014-09-18T10:01:01Z 2012-08 2012-09-18T21:18:24Z 2012-08 For finite group presentations, the word problem is solvable if and only if the Dehn function is computable. Additionally, the bounded word problem is always solvable. For finitely generated decidable group presentations, this is not always the case. The main result of the present work is to determine whether there exist examples of finitely generated decidable group presentations for each combination of solvability/unsolvability of the word problem, solvability/unsolvability of the bounded word problem, and computability/uncomputability of the Dehn function. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-07-11T14:56:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Cummins_Desmond.pdf: 741090 bytes, checksum: 806fff69ab6f60e40d6c1f5fa170f03c (MD5) Made available in DSpace on 2012-09-18T21:18:24Z (GMT). No. of bitstreams: 2 Cummins_Desmond.pdf: 741090 bytes, checksum: 806fff69ab6f60e40d6c1f5fa170f03c (MD5) license.txt: 4065 bytes, checksum: ad4ba3ebe7f6afbaec95d0c79cabe717 (MD5) Restriction data tranferred 2014-07-01T11:35:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: 2014-09-18 16:21:01 UTC Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Seth Robbins (srobbins@illinois.edu) on 2012-09-18T21:21:09Z Item is restricted until 2014-09-18T21:21:01Z U of I Only Restriction Lifted for Item 34737 on 2014-09-18T10:01:01Z. http://hdl.handle.net/2142/34463 en Copyright 2012 Desmond Cummins Group Theory Dehn Function Word Problem Bounded Word Problem The Dehn function, word problem, and bounded word problem for finitely generated decidable group presentations Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD