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A Boolean function can be represented as a rooted, directed, acyclic graph, which consists of several (decision) nodes and two terminal nodes. The two terminal nodes are labeled 0 (FALSE) and 1 (TRUE). Each (decision) node is labeled by a Boolean variable and has two child nodes called low child and high child.
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
A Boolean circuit over a basis B, with n inputs and m outputs, is then defined as a finite directed acyclic graph. Each vertex corresponds to either a basis function or one of the inputs, and there is a set of exactly m nodes which are labeled as the outputs.
A Boolean circuit with input bits is a directed acyclic graph in which every node (usually called gates in this context) is either an input node of in-degree 0 labelled by one of the input bits, an AND gate, an OR gate, or a NOT gate. One of these gates is designated as the output gate.
A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph of the following form: Leaves are labeled with (true), (false), or a Boolean variable.
The total influence of a Boolean function is also the average sensitivity of the function. The sensitivity of a Boolean function at a given point is the number of coordinates such that if we flip the 'th coordinate, the value of the function changes. The average value of this quantity is exactly the total influence.
This is a list of topics around Boolean algebra and propositional logic. ... And-inverter graph; Logic gate; Boolean analysis; Theorems and specific laws
The graph has a c-clique if and only if the formula is satisfiable. [ 11 ] There is a simple randomized algorithm due to Schöning (1999) that runs in time (4/3) n where n is the number of variables in the 3-SAT proposition, and succeeds with high probability to correctly decide 3-SAT.