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Boolean function; Boolean-valued function; Boolean-valued model; Boolean satisfiability problem; Boolean differential calculus; Indicator function (also called the characteristic function, but that term is used in probability theory for a different concept) Espresso heuristic logic minimizer; Logical matrix; Logical value; Stone duality; Stone ...
In computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language can be decided by a family of Boolean circuits, one circuit for each possible input length. Boolean circuits are defined in terms of the logic gates they contain.
Logic optimization is a process of finding an equivalent representation of the specified logic circuit under one or more specified constraints. This process is a part of a logic synthesis applied in digital electronics and integrated circuit design.
It has been called the "fundamental theorem of Boolean algebra". [1] Besides its theoretical importance, it paved the way for binary decision diagrams (BDDs), satisfiability solvers, and many other techniques relevant to computer engineering and formal verification of digital circuits.
The circuit on the left is satisfiable but the circuit on the right is not. In theoretical computer science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean circuit has an assignment of its inputs that makes the output true. [1]
The first proof of this theorem used the invariance principle in conjunction with an isoperimetric theorem of Borell in Gaussian space; since then more direct proofs were devised. [ 16 ] [ 17 ] Majority is Stablest implies that the Goemans–Williamson approximation algorithm for MAX-CUT is optimal, assuming the unique games conjecture .
In digital electronics terminology, the binary NAND gate (↑) and the binary NOR gate (↓) are the only binary universal logic gates. The following are the minimal functionally complete sets of logical connectives with arity ≤ 2: [11] One element {↑}, {↓}. Two elements
In computer science and formal methods, a SAT solver is a computer program which aims to solve the Boolean satisfiability problem.On input a formula over Boolean variables, such as "(x or y) and (x or not y)", a SAT solver outputs whether the formula is satisfiable, meaning that there are possible values of x and y which make the formula true, or unsatisfiable, meaning that there are no such ...