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The stochastic sequential machine is invariably treated as the stochastic extension of the completely-specified deterministic machine. This paper investigates the incompletely-specified finite-state stochastic sequential machine from the viewpoint of machine equivalence and reduction. Definitions are chosen and procedures developed so that they reduce to the conventional froms in the special cases...
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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