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...

We will study the question about decidability for Boolean algebras with first elementary characteristic one. The main problem is sufficient conditions for decidability of Boolean algebras with recursive representation for extended signature by definable predicates. We will use the base definitions on recursive and constructive models from [2, 4-6, 10, 1 l] but on Boolean algebras from [I, 81. @...

The Boolean network can be used as a mathematical model for gene regulatory networks. An attractor, which is a state of a Boolean network repeating itself periodically, can represent a stable stage of a gene regulatory network. It is known that the problem of finding an attractor of the shortest period is NP-hard. In this article, we give a fixed-parameter algorithm for detecting a singleton at...

A rapidly advancing field, image compression has seen many recent developments. A number of well-known compression algorithms dominate the world of lossy compression, but in the realm of lossless compression, fewer techniques have been explored. The most successful lossy compression methods are based on transform methodologies, commonly involving the KLT, cosine, and wavelet transforms. However...

Nuances of truth represent a robust paradigm in the framework of many-valued logics [1]. The idea of nuancing states that a many-valued object is uniquely determined by some Boolean objects, its nuances, and it is called the determination principle. However, a many-valued object cannot be recovered only from its Boolean nuances. This idea goes back to Gr. C. Moisil [4] and it is mathematically ...