A Contribution to the Theory of Boolean Algebras

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A Contribution to the Theory of Boolean Algebras

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dc.contributor.advisor Kurepa, Đuro
dc.contributor.author Tošić, Ratko en_US
dc.date.accessioned 2009-12-03T12:22:22Z
dc.date.available 2009-12-03T12:22:22Z
dc.date.issued 1978
dc.identifier.uri http://hdl.handle.net/123456789/356
dc.description.abstract The thesis consists of five chapters. In Chapter 1 definitions and well-known results from the theory of Boolean algebras and Boolean functions are given. In Chapter 2 of the thesis some properties of Boolean functions, which preserve constants under finite Boolean algebras, are presented by using the component representation. Their consequences about the number of Boolean’s functions are also given. The theorems which are the generalization of Scognmaiglio’s theorem and Andreoli’s theorem for Boolean functions with one variable, are proved in Chapter 3. The following new notions are introduced for monotone logical functions: the profile, the level, homogeneous, the corresponding matrix, etc. Some properties of these functions are shown and some consequences about the number of homogeneous monotone logical functions are presented. In Chapter 4 the applications of monotone Boolean functions in solving the problems of search theory (a branch of the theory of information) are presented. It is shown that the general problem of a type is, in fact, the problem of identifications of homogeneous monotone Boolean functions of the given profile by checking the value of that function for combinations of values of variables. Optimal or almost optimal solutions for some profiles are shown. It is also shown that monotonic logical functions are natural instrument for the generalization of these problems. Some open problems are presented in Chapter 5. en
dc.description.provenance Made available in DSpace on 2009-12-03T12:22:22Z (GMT). No. of bitstreams: 1 phdRatkoTosic.pdf: 3843270 bytes, checksum: 6877129f36f1acff60d2559ad71df638 (MD5) en
dc.publisher Belgrade en_US
dc.title A Contribution to the Theory of Boolean Algebras en_US
dc.title.alternative Prilog teoriji Booleovih algebri sr
mf.subject.keywords Boolean algebras, Boolean functions, search theory
mf.contributor.committee Slaviša Prešić
mf.contributor.committee Koriolan Gilezan

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