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- W2296328287 abstract "A combinational circuit realizing switching function f(x) may be regarded as a solution verifier for Boolean equation f(x) = 1. (*) The output of circuit is 1, that is, if and only if input-vector x is a solution for (*). We use term to denote an approach to circuit synthesis based on (*) rather than on function f(x). The central problem of equational logic is to find a system of equations gi(x) = hi(x) (i = 1,2,...,k), of simplest possible form, that has same solutions as (*). Given such a k-equation system, f(x) may be realized as output of a k-wide digital comparator whose inputs are 2k g's and h's constituting system. The problem of finding a simple system of equations equivalent to a given equation was investigated more than a century ago by Willian Stanley Jevons, who called it the inverse problem of logic. It was thought by Jevons and other 19th century logicians that inverse problem is always tentative, i.e., that it does not admit of algorithmic solution. It is shown in this paper, however, that inverse problem may be solved as a covering problem by use of table of consequences of Poretsky. As presently formulated, this approach is limited in practical utility by large size of tables involved. It appears that a practical solution technique requires a reformulation of inverse problem." @default.
- W2296328287 created "2016-06-24" @default.
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- W2296328287 date "1974-12-01" @default.
- W2296328287 modified "2023-09-28" @default.
- W2296328287 title "Equational Logic" @default.
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- W2296328287 doi "https://doi.org/10.1109/t-c.1974.223841" @default.
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