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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...
The problem of assigning a probability to each string of a language L(G) generated by a grammar G is considered. Two methods are considered. One method assigns a probability to each production associated with G and the other assigns the probabilities on the basis of particular features of the language. Several necessary conditions that must be satisfied by these probability assignment techniques if...
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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