System functions and their decision problems

• Main Author: Thuraisingham, M. B.
• Published: Swansea University 1979
• Subjects: 510
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639238

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.