### Statistical Complexity of Algorithms for Boolean Function MinimizationStatistical Complexity of Algorithms for Boolean Function Minimization

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 Author Mileto, Franco ♦ Putzolu, Gianfranco Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1965 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract The first problem in a two level Boolean minimization is the determination of the prime $\textit{k}-cubes.$ This paper is concerned with the estimation of the statistical complexity of some well-known algorithms which solve this problem. Formulas are given for the average number of comparison operations among $\textit{k}-cubes$ occurring in Quine's method and in Mc-Cluskey's method; these quantities provide indications of the average execution time of computer programs based on the corresponding algorithms. Numerical values are given and commented on.Formulas are also obtained for the variance of the number of $\textit{k}-cubes$ and the variance of the number of cubes of a Boolean function; in fact the calculation of these quantities is strictly related to that of the average number of comparison operations among $\textit{k}-cubes.These$ variances give an idea of the probable error made by using the corresponding average values (obtained in a previous paper by the authors) to make forecasts. It turns out that this error is quite small. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1965-07-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 12 Issue Number 3 Page Count 12 Starting Page 364 Ending Page 375

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Source: ACM Digital Library