The research of Boolean index sets of graphs is one of the important graph theory in the graph theory. Boolean index sets of graphs are to use the vertex sets and the edge sets of graphs to study the characteristics of various graphs and their inherent characteristics through corresponding the mapping function to 2 Z . Its theory can be applied to information engineering, communication networks...

probabilistic boolean networks the modeling and control of probabilistic boolean networks the modeling and control of probabilistic boolean networks: the modeling and control probabilistic boolean networks society for industrial probabilistic boolean networks the modeling and control of probabilistic control of boolean networks with multiple from boolean to probabilistic boolean networks as mod...

We investigate the complexity of the tree share model of Dockins et al., which is used to reason about shared ownership of resources in concurrent programs. We obtain the precise Berman complexity for the first-order theory of the Boolean algebra of tree shares with constants, which is STA(∗, 2 O(1) , n)-complete. For the first-order theory over the “relativization” multiplication operator on t...

In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f = I. We describe several generalisations of well-known results in the theory of boolean functions, including quantum property testing; a quantum version of the Goldreich-Levin algorithm for finding the large Fourier coefficients of boolean functions; and two quantum v...

We answer three problems by J. D. Monk on cardinal invariants of Boolean algebras. Two of these are whether taking the algebraic density πA resp. the topological density dA of a Boolean algebra A commutes with formation of ultraproducts; the third one compares the number of endomorphisms and of ideals of a Boolean algebra. In set theoretic topology, considerable effort has been put into the stu...

In this article we investigate the notion and basic properties of Boolean algebras and prove the Stone’s representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completeness theorem in propositional logic will be given using Stone’s theorem from Boolean algebra. We mention here that the method we used can also be e...

objective: to classify different types of acute leukemia based on cooperative game theory and shapley value. materials and methods: in this study, patients data were collected from flow cytometry tests of the iran blood transfusion organization (ibto) have been used. 304 different diagnosed samples in 8 classes of acute leukemia were investigated. samples were initially in numerical format. i...

Classi cation is one of major tasks in case-based reasoning(CBR) and many studies have been done for analyzing properties of case-based classi cation [1, 14, 10, 15, 12, 9, 13, 7]. However, these studies only consider numerical similarity measures whereas there are other kinds of similarity measure for di erent tasks. Among these measures, HYPO system [2, 3] in a legal domain uses a similarity ...

Rough set theory is an important technique for knowledge discovery in databases, and its algebraic structure is part of the foundation of rough set theory. In this paper, we present the structures of the lower and upper approximations based on arbitrary binary relations. Some existing results concerning the interpretation of belief functions in rough set backgrounds are also extended. Based on ...

A boolean term order is a total order on subsets of [n] = {1,. .. , n} such that ∅ ≺ α for all α ⊆ [n], α = ∅, and α ≺ β ⇒ α ∪ γ ≺ β ∪ γ for all γ with γ ∩ (α ∪ β) = ∅. Boolean term orders arise in several different areas of mathematics, including Gröbner basis theory for the exterior algebra, and comparative probability. The main result of this paper is that boolean term orders correspond to o...