Circuits over natural numbers are a mathematical model used in studying computational complexity theory. They are a special case of circuits. The object...

Goldbach's conjecture. It is a natural extension of the circuits over sets of natural numbers when the considered set contains also negative integers...

depth of circuits that can compute them. Arithmetic circuit complexity Boolean circuit Circuit complexity Circuits over sets of natural numbers The complexity...

If one defines natural numbers to be the cardinalities of finite sets (the cardinality of a set is the number of elements in the set), then it is appropriate...

is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in...

of the coordinates of two points in space. In fact, Ferdinand Georg Frobenius later proved in 1877 that for a division algebra over the real numbers to...

characterized as the branch of mathematics dealing with countable sets (finite sets or sets with the same cardinality as the natural numbers). However, there is...

isomorphism theorem can be stated as follows: "For all sets A , B {\displaystyle A,B} of natural numbers, A ≡ B ⟺ A ≡ 1 B {\displaystyle A\equiv B\iff A\equiv...

isomorphic to a field of sets. In the 1930s, while studying switching circuits, Claude Shannon observed that one could also apply the rules of Boole's algebra...

arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs either variables or numbers, and is...

description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely...

a circuit by an independent low-power signal and to control several circuits by one signal. They were first used in long-distance telegraph circuits as...

two sets of values. The set type constructor (written set of T where T is a predefined type) constructs the type composed of all finite sets of values...

the set S whose independent sets are the independent sets of M that are contained in S. Its circuits are the circuits of M that are contained in S and...

linear integrated circuits 4000-series integrated circuits, List of 4000-series integrated circuits 7400-series integrated circuits, List of 7400-series integrated...

element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted...

have not surpassed the binary circuits. They wrote in the conclusion that Multi-valued circuits and two-valued circuits must not be seen as competitors...

(SIMD) instruction sets (Streaming SIMD Extensions, AltiVec etc.) where 128-bit vector registers are used to store several smaller numbers, such as four 32-bit...

transistors and integrated circuits, the latter principally by photolithography and often on printed circuit boards.[citation needed] Circuit boards are assembled...

first planar monolithic integrated circuit (IC) chip was demonstrated in 1960. The idea of integrating electronic circuits into a single device was born when...

(1954). The Boy's Book of Crystal Sets. London: Bernard's. is a collection of 12 circuits Purdie, Ian (1999). "A Basic Crystal Set". Ian Purdie's Amateur...

binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one). A binary...

theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements...

electromechanical device consisting of one or more sets of movable electrical contacts connected to external circuits. When a pair of contacts is touching current...

signals, including thermal and shot noise, jitter and metastability of electronic circuits, Brownian motion, and atmospheric noise. Researchers also used the...

interpretation. For example, theories of arithmetic such as Peano arithmetic are satisfiable because they are true in the natural numbers. This concept is closely...

valve, a so-called "tuned circuit". Broadband circuits require flat response over a wide range of frequencies. RF circuits by contrast are typically required...

sets concerned the design of sequential logic circuits, in which signals can propagate in cycles through the circuit instead of always progressing from...

on the theory of graphs. ˝ Bull. Amer. Math. Soc. 53 292–294.}} Beck, József (1990). "On Size Ramsey Number of Paths, Trees and Circuits. II". In Nešetřil...

fingertip Electrical resonance of tuned circuits in radios and TVs that allow radio frequencies to be selectively received Creation of coherent light by optical...