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Original and simplified example circuit. While there are many ways to minimize a circuit, this is an example that minimizes (or simplifies) a Boolean function. The Boolean function carried out by the circuit is directly related to the algebraic expression from which the function is implemented. [7]
This expression says that the output function f will be 1 for the minterms ,,,, and (denoted by the 'm' term) and that we don't care about the output for and combinations (denoted by the 'd' term). The summation symbol ∑ {\displaystyle \sum } denotes the logical sum (logical OR, or disjunction) of all the terms being summed over.
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 ...
Examples of don't-care terms are the binary values 1010 through 1111 (10 through 15 in decimal) for a function that takes a binary-coded decimal (BCD) value, because a BCD value never takes on such values (so called pseudo-tetrades); in the pictures, the circuit computing the lower left bar of a 7-segment display can be minimized to a b + a c by an appropriate choice of circuit outputs for ...
[4] [3] It is a resource and performance efficient algorithm aimed at solving the heuristic hazard-free two-level logic minimization problem. [13] Rather than expanding a logic function into minterms, the program manipulates "cubes", representing the product terms in the ON-, DC-, and OFF- covers iteratively.
For example, given the Boolean expression: = () will become: = () (), with ,,, …, being all distinct variables. This relaxes the problem by introducing new variables into the Boolean expression, [ 4 ] which has the effect of removing many of the constraints in the expression.
Note that minimization of a submodular function is a polynomially solvable problem independent on the presentation form, for e.g. pesudo-Boolean polynomials, opposite to maximization of a submodular function which is NP-hard, Alexander Schrijver (2000).
A pseudo-Boolean function: {,} is said to be representable if there exists a graph = (,) with non-negative weights and with source and sink nodes and respectively, and there exists a set of nodes = {, …,} {,} such that, for each tuple of values (, …,) {,} assigned to the variables, (, …,) equals (up to a constant) the value of the flow determined by a minimum cut = (,) of the graph such ...