Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639238
Title: System functions and their decision problems
Author: Thuraisingham, M. B.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1979
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Abstract:
The study of System Functions arose as a consequence of the investigation of one-one equivalence between general combinatorial decision problems. For each combinatorial system such as a Semi Thus System, Thus 1 System, Turing Machine, Markov Algorithm, etc., there exists a corresponding system function. Thus, decision problems defined for these combinatorial systems can also be defined for system functions. Here, a Generalized Class of Formulas is defined in terms of a first-order language such that each formula in this class corresponds to a decision problem for system functions. Consequently, a large number of decision problems are scanned simultaneously in order to investigate one-one equivalence between general combinatorial decision problems. These formulas are analysed to determine whether they are (a) nonsimple; (b) either finite, cofinite, or cylinders. Also, several simple decision problems and nonrecursive and noncylindrical decision problems for system functions are constructed. Furthermore, the concept of semi-cylinder has been extended to that of n-cylinder in order to construct some of these nonrecursive and noncylindrical decision problems. As a consequence of the investigation on degrees of combinatorial decision problems, some independence and dependence relations between decision problems for system functions are obtained. Finally, an application of our concept of n-cylinder in Recursive Function Theory is given.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.639238  DOI: Not available
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