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Parity only depends on the number of ones and is therefore a symmetric Boolean function.. The n-variable parity function and its negation are the only Boolean functions for which all disjunctive normal forms have the maximal number of 2 n − 1 monomials of length n and all conjunctive normal forms have the maximal number of 2 n − 1 clauses of length n.
The circuit for the Millionaires' Problem is a digital comparator circuit (which is a chain of full adders working as a subtractor and outputting the carry flag). A full adder circuit can be implemented using only one AND gate and some XOR gates. This means the total number of AND gates for the circuit of the Millionaires' Problem is equal to ...
The size of a circuit is the number of gates it contains and its depth is the maximal length of a path from an input gate to the output gate. There are two major notions of circuit complexity. [1] The circuit-size complexity of a Boolean function is the minimal size of any circuit computing .
In computational complexity theory, CC (Comparator Circuits) is the complexity class containing decision problems which can be solved by comparator circuits of polynomial size. Comparator circuits are sorting networks in which each comparator gate is directed, each wire is initialized with an input variable, its negation, or a constant, and one ...
By Lemma 1, we get a branching program for A outputting the identity or α, i.e. α-computing ¬A=C. If the circuit C outputs A∧B for circuits A and B, join the branching programs that γ-compute A, δ-compute B, γ −1-compute A, and δ −1-compute B for a choice of 5-cycles γ and δ such that their commutator ε=γδγ −1 δ −1 is ...
In 1984 Furst, Saxe, and Sipser showed that calculating the parity of the input bits (unlike the aforementioned addition/subtraction problems above which had two inputs) cannot be decided by any AC 0 circuits, even with non-uniformity. [5] [1] It follows that AC 0 is not equal to NC 1, because a family of circuits in the latter class can ...
Comparators are closely related to operational amplifiers, but a comparator is designed to operate with positive feedback and with its output saturated at one power rail or the other. If necessary, an op-amp can be pressed into service as a poorly performing comparator, but its slew rate will be impaired.
In physics, the C parity or charge parity is a multiplicative quantum number of some particles that describes their behavior under the symmetry operation of charge conjugation. Charge conjugation changes the sign of all quantum charges (that is, additive quantum numbers ), including the electrical charge , baryon number and lepton number , and ...