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An and-inverter graph (AIG) is a directed, acyclic graph that represents a structural implementation of the logical functionality of a circuit or network.An AIG consists of two-input nodes representing logical conjunction, terminal nodes labeled with variable names, and edges optionally containing markers indicating logical negation.
In the 1960s, E. F. Rent, an IBM employee, found a remarkable trend between the number of pins (terminals, T) at the boundaries of integrated circuit designs at IBM and the number of internal components (g), such as logic gates or standard cells. On a log–log plot, these datapoints were on a straight line, implying a power-law relation ...
The AND gate is a basic digital logic gate that implements the logical conjunction (∧) from mathematical logic – AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If all of the inputs to the AND gate are not HIGH, a LOW (0) is outputted.
In first-order logic with equality, counting quantifiers can be defined in terms of ordinary quantifiers, so in this context they are a notational shorthand. However, they are interesting in the context of logics such as two-variable logic with counting that restrict the number of variables in formulas. Also, generalized counting quantifiers ...
It was the first practical AND circuit, precursor of the AND logic circuits of electronic computers. To detect the voltage pulse produced by the coincidence circuit when a coincidence event occurred, Rossi first used earphones and counted the ‘clicks’, and soon an electro-mechanical register to count the coincidence pulses automatically.
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device [1] (see ...
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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 f {\displaystyle f} is the minimal size of any circuit computing f {\displaystyle f} .