2.1.3 Boolean Algebra A Boolean function, f(x1, x2, …, xn) maps an n tuple of (0,1) values to {0,1}. Boolean algebra is a convenient notation for representing Boolean functions. Boolean algebra uses the connectives ·, +, and −. For example, the and function of two variables...
Essentially, these circuits use feedback loops where the output of certain gates is looped back as an input. This allows the flip-flop to maintain its state (store a 1 or a 0) until it receives a signal to change. Basic memory cells in computers can store information this way. Each ...
• N<N is the family of all finite sequences of natural numbers, • diam(A) is the diameter of a set A in the given metric space. 2.1. Borel measures By a Borel measure on a compactum X we mean a countably additive measure μ:Bor(X)→[0,∞], defined on the σ-algebra of...
Game theory is a mathematical tool to study the behavior of independent agents in strategic interaction. Reasoning and communication have an essentially strategic aspect. Game theoretic is thus a suitable tool to illuminate the interactive aspects of logic and language. ...
In contrast, the case of \mathbb {F}_2, is precisely the case that we are interested in when considering Boolean circuits, which require generating Beaver triples over \mathbb {F}_2. Additionally, the concrete efficiency of an FFT computed over the group algebra remains unclear, since Bombar...
Also related to the KKL theorem, Friedgut’s Junta theorem [Fri98] states that a Boolean function with a bounded total influence essentially depends on few coordinates. More precisely, a Boolean functionis called ak-junta, forindependent ofn, if it depends on at mostkcoordinates. When, the ...
That dapper Englishman is George Boole (1815-1864). He was the father of five children. He was also “the father of the information age.” George invented Boolean algebra (remember algebra?). This breaks down every calculation into “true” or “false.” Then you add these statements togeth...
Boolean logic and operators (based on Boolean algebra) are used in most information databases, providing the ability to combine synonyms and variant concepts together to access relevant items. AND, OR, and NOT are the basic Boolean connectors. Nesting is used to show search logic and the order...
The nonstandard approach to fuzzy sets on the contrary is based on a non-Cantorian framework, which essentially amounts to viewing the eternally constant Cantorian-Platonic universe through two observers: the absolute Cantorian and the local non-Cantorian [5]. The construction of such a theory...
In [3], the connection between the algebra of conditional sets [1,4] and Boolean valued analysis [5] was provided. In the present paper, we provide a similar connection for the framework of random set theory [2]. We aim to show that the well-known set-theoretic techniques of Boolean ...