Pseudo-Boolean Programming and Applications: Presented at by Petru L. Ivănescu (auth.)

By Petru L. Ivănescu (auth.)

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Extra info for Pseudo-Boolean Programming and Applications: Presented at the Colloquium on Mathematics and Cybernetics in the Economy, Berlin, October 1964

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N) o = x. 8) J F (yO ,yO o o) i'''" ; Zl'''"Zn = G ( o Xl,... we obtain the optimal solution of the initial problem. The computational solving concrete sibly reduced, time required by the above method in transportation problems, turned out to be sen- compared to that required by other methods. Chapter 9 Applications to Switching Algebra In this chapter we shall describe a method of determining all absolute minima of a Boolean function. arises frequently in switching algebra where it is interpreted as the problem of determining given program of functioning smallest number of relays a switching circuit satisfying and containing slightly different, methods for determinating available for instance a the (this criterion of economcity may be present also in other, are This problem forms).

14. /37/. : "R@solution Bool@enne d'op@rations arithm@tiques sur les entiers non n@gatifs et applications aux programmes lin@aires en nombres entiers", SMA, Paris, Mars 196o, (Mimeographed). /38/. 7ol-7o2. - 43 - /39/. 44o-~51. /4o/. L. Graves and Ph. Wolfe, McGraw-Hill,1963. /41/. : "A Theorem on Flows in Networks", Pacific J. ,7,1957,1o73-1o82. /42/. : "The Theory of Linear Economic Models", McGrawHill, 196o. /43/. 5. /44/. GOMORY, R. l, Issue, 36, Abstract 553-19o. /45/. : "Distinct Representatives of Subsets", Bull.

2) is called prime if deleting any letter or term of it, it ceases to be an implicant. ,pm may be easily deter- mined with a method of MacCluskey /88/. 3) the number of letters contained in P j, and putting m j-1 we have (/72/): Io) In fact the method permits also the choice of any other criterion of minimization, (see /72/). ,Xn), and any absolut minimum of f is of this type. Chapter lo Minimal decomposition of finite partially ordered sets in chains The aim of this chapter is to show that the problem of finding the number N of chains in a minimal decomposition of a finite partially ordered set S, as well as that of actually determining those chains, may be reduced to one of minimizing a pseudo-Boolean function.

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