Type of Document	Dissertation
Author	Kozik, Marcin Andrzej
URN	etd-09292004-212720
Title	On some complexity problems in finite algebras
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Professor Ralph McKenzie Committee Chair Professor Alan Peters Committee Member Professor Alexander Ol'shanskii Committee Member Professor Constantine Tsinakis Committee Member Professor Mark Sapir Committee Member
Keywords	gamma function beta function membership problem universal algebra computational complexity
Date of Defense	2004-09-24
Availability	unrestricted
Abstract This work contains constructions of finite algebras which are "complex" according to three different complexity measures. These constructions are modifications of the construction of Ralph McKenzie's A(T). They produce finite algebras that "model" computations of Turing machines on various inputs. In this way, we obtain a finite algebra generating a variety with PSPACE--complete membership problem and another algebra with exponentially growing gamma function. The final construction produces a finite algebra that is able to model a computation of a Turing machine on an exponentially long tape. This gives an example of a finite algebra with EXPSAPCE--hard membership problem and a doubly exponentially growing beta function. Examples of finite algebra of such complexity classes were not known before.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    ExpSpace.pdf 398.21 Kb 00:01:50 00:00:56 00:00:49 00:00:24 00:00:02