On the Theory of Boolean Formulas: Minimal Including Sums, I

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Previous article Next article On the Theory of Boolean Formulas: Minimal Including Sums, IE. W. Samson and L. CalabiE. W. Samson and L. Calabihttps://doi.org/10.1137/0111017PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] W. V. Quine, The problem of simplifying truth functions, Amer. Math. Monthly, 59 (1952), 521–531 MR0051191 0048.24503 CrossrefGoogle Scholar[2] Edward W. Samson and , Burton E. Mills, Circuit minimization: algebra and algorithms for new Boolean canonical expressions, Tech. Rep. 54–21, Communications Laboratory, Electronics Research Directorate, Air Force Cambridge Research Center, Cambridge, Mass., 1954, 54– MR0073454 Google Scholar[3] E. W. Samson and , R. K. mueller, Circuit minimization: Minimal and irredundant Boolean sums by alternative set method, TR-55–109, Air Force Cambridge Research Center, 1955 Google Scholar[4] Edward W. Samson and , Rolf K. Mueller, Circuit minimization: sum to one process for irredundant sums, Tech. Rep. 55-118, Communications Laboratory, Electronics Research Directorate, Air Force Cambridge Research Center, Cambridge, Mass., 1955vii+16 MR0074956 Google Scholar[5] Raymond J. Nelson, Simplest normal truth functions, J. Symb. Logic, 20 (1955), 105–108 MR0072073 0066.25602 CrossrefGoogle Scholar[6] Kurt Bing, On simplifying truth-functional formulas, J. Symb. Logic, 21 (1956), 253–254 MR0082937 0072.00104 CrossrefGoogle Scholar[7] W. V. Quine, On cores and prime implicants of truth functions, Amer. Math. Monthly, 66 (1959), 755–760 MR0108439 0201.32203 CrossrefGoogle Scholar[8] J. A. Riley, Foundations for a general theory of Boolean formulas, SR-3-3471 (AFCRL-TN-60-970), Parke Mathematical Laboratories, 1960 Google Scholar[9] J. Paul Roth, Algebraic topological methods for the synthesis of switching systems. I, Trans. Amer. Math. Soc., 88 (1958), 301–326 MR0097285 0083.13103 CrossrefGoogle Scholar[10] E. W. Samson and , L. Calabi, Research and Algorithms in the Theory of Boolean Formulas, Proc. 3d Symp. Switching Circuit Theory and Logical Design, A.I.E.E., Chicago, Illinois, 1962 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails On the Theory of Boolean Formulas: Construction of the Set of the Formulas of Minimal CostL. CalabiJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 3 | 13 July 2006AbstractPDF (538 KB)On the Theory of Boolean Formulas: Minimal Including Sums, IIE. W. Samson and L. CalabiJournal of the Society for Industrial and Applied Mathematics, Vol. 11, No. 2 | 13 July 2006AbstractPDF (997 KB) Volume 11, Issue 2| 1963Journal of the Society for Industrial and Applied Mathematics205-519 History Submitted:10 July 1961Published online:13 July 2006 InformationCopyright © 1963 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0111017Article page range:pp. 212-223ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics