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The Computer Journal 1980 23(1):73-77; doi:10.1093/comjnl/23.1.73
© 1980 by British Computer Society
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The size of arrays for a prime implicant generating algorithm

Y. Igarashi *

Department of Computer Science, University of Gunma, Kiryu-City, Gunma-Prefecture, Japan

A number of interesting combinatorial problems have arisen by investigating a computer implementation of a prime implicant generator called the star-algorithm. These problems have been motivated by the necessity of estimating suitable sizes of arrays to store intermediate results when the algorithm is written in a computer language such as ALGOL 60. Bn(r) denotes the set of r-cubes of the n-variable Boolean algebra and {circledast} denotes the star-product. P(Bn(r))=#({b|b {epsilon}Bn(r) and a {circledast}b!=&}), where #(S) is the number of elements of set S, a is an arbitrary element of Bn(r), and a {circledast}b !=& means that the star-product of a and b is a cube. The main combinatorial result in this paper is that for all 0<{epsilon}, K1(n33/4)n≤ max{P(Bn(r))|0≤r≤n}≤k2(33/4 +{epsilon})n. where k1 and k2 are constants independent of n.

Received June 1978.

* Now at Department of Computer Science, University of Gunma, Kiryu-city, Gunma-prefecture, Japan.

§ Computer Science Division, Department of Mathematics, The City University, London EC1V 4PB


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