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All concrete Boolean algebras satisfy the laws (by proof rather than fiat), whence every concrete Boolean algebra is a Boolean algebra according to our definitions. This axiomatic definition of a Boolean algebra as a set and certain operations satisfying certain laws or axioms by fiat is entirely analogous to the abstract definitions of group ...
Redundancy, by definition, requires extra parts (in this case: logical terms) which raises the cost of implementation (either actual cost of physical parts or CPU time to process). Logic redundancy can be removed by several well-known techniques, such as Karnaugh maps, the Quine–McCluskey algorithm, and the heuristic computer method.
Boolean algebra is a mathematically rich branch of abstract algebra. Stanford Encyclopaedia of Philosophy defines Boolean algebra as 'the algebra of two-valued logic with only sentential connectives, or equivalently of algebras of sets under union and complementation.' [1] Just as group theory deals with groups, and linear algebra with vector spaces, Boolean algebras are models of the ...
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties of both set operations and logic operations. A Boolean algebra can be seen as a generalization of a power set algebra or a field of sets, or its elements can be viewed as generalized ...
Boole's expansion theorem; Boolean algebras canonically defined; Boolean conjunctive query; Boolean data type; Boolean differential calculus; Boolean domain; Boolean expression; Boolean function; Boolean matrix; Boolean prime ideal theorem; Boolean ring; Boolean satisfiability algorithm heuristics; Boolean satisfiability problem; Boolean-valued ...
Boolean algebra An area of algebra in which the values of the variables are the truth values true and false, typically used in computer science, logic, and mathematical logic. Boolean negation A form of negation where the negation of a non-true proposition is true, and the negation of a non-false proposition is false. [34] [35] [36] Boolean ...
Schaefer's dichotomy theorem states that, for any restriction to Boolean functions that can be used to form these subformulas, the corresponding satisfiability problem is in P or NP-complete. The membership in P of the satisfiability of 2CNF, Horn, and XOR-SAT formulae are special cases of this theorem. [14]
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.