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Let Φ be any abstract measure of computational complexity, and let L denote the specific measure of memory resource (tape) on one tape Turing machines. Denote by Rt( )Φ the class of all total functions whose Φ-complexity is bounded by the function t( ) almost everywhere. Call such classes Φ-complexity classes. We are interested in relationships among these classes, under proper set inclusion (⊂)....
Some properties of multiprocessing systems, i.e. computing systems in which a set of computational elements share a pool of storage elements are investigated. In particular, the conditions for the output-functionality of these systems are studied, where a computing systems is defined as being output-functional when it produces the same sequence of outputs for the same program, initial state, and input...
This paper continues investigations pertaining to recursive bounds on computing resources (such as time or memory) and the amount by which these bounds must be increased if new computations are to occur within the new bound. The paper proves that no recursive operator can increase every recursive bound enough to reach new computations. In other words, given any general recursive operator F[ ], there...
This paper develops techniques for establishing a lower bound on the number of arithmetic operations necessary for sets of simple expressions. The techniques are applied to matrix multiplication. A modification of Strassen's algorithm is developed for multiplying n × p matrices by p × q matrices. The techniques are used to prove that this algorithm minimizes the number of multiplications for a few...
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