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Arithmetic circuit complexity information


In computational complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs either variables or numbers, and is allowed to either add or multiply two expressions it has already computed. Arithmetic circuits provide a formal way to understand the complexity of computing polynomials. The basic type of question in this line of research is "what is the most efficient way to compute a given polynomial ?"

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Arithmetic circuit complexity

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computational complexity theory, arithmetic circuits are the standard model for computing polynomials. Informally, an arithmetic circuit takes as inputs...

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Circuit complexity

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In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according...

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Arithmetic logic unit

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In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers...

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VNP

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VNP may refer to: VNP, standing for Valiant's NP, an arithmetic circuit complexity class Ventricular Natriuretic Peptide, an alternative name for Brain...

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Boolean circuit

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computational complexity theory and circuit complexity, a Boolean circuit is a mathematical model for combinational digital logic circuits. A formal language...

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Fast Fourier transform

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sometimes called the "arithmetic complexity" (although in this context it is the exact count and not the asymptotic complexity that is being considered)...

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Computational complexity theory

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communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in...

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List of computability and complexity topics

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Exponentiating by squaring Addition chain Scholz conjecture Presburger arithmetic Arithmetic circuits Algorithm Procedure, recursion Finite state automaton Mealy...

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Arithmetic

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Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider...

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Computational complexity of matrix multiplication

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lower bound for matrix-multiplication complexity is Ω(n2 log(n)), for bounded coefficient arithmetic circuits over the real or complex numbers, and is...

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Polynomial identity testing

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an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computational complexity required...

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Integrated circuit

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based electronics. Photonic integrated circuits that use light such as Lightelligence's PACE (Photonic Arithmetic Computing Engine) also being developed...

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Proof complexity

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Computational complexity Circuit complexity Communication complexity Mathematical logic Proof theory Complexity classes NP (complexity) coNP Cook, Stephen;...

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Polynomial evaluation

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parallelization on modern computer architectures Arithmetic circuit complexity theory studies the computational complexity of evaluating different polynomials. Carnicer...

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Quantum complexity theory

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computation, such as the quantum circuit model or the equivalent quantum Turing machine. One of the main aims of quantum complexity theory is to find out how...

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Affine arithmetic

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(mathematics), process control, worst-case analysis of electric circuits, and more. In affine arithmetic, each input or computed quantity x is represented by a...

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P versus NP problem

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"Computational Complexity of Games and Puzzles". Fischer, Michael J.; Rabin, Michael O. (1974). "Super-Exponential Complexity of Presburger Arithmetic". Proceedings...

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Switching lemma

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computational complexity theory, Håstad's switching lemma is a key tool for proving lower bounds on the size of constant-depth Boolean circuits. It was first...

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BIT predicate

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also the same as the circuit complexity class DLOGTIME-uniform AC0. Here, AC0 describes the problems that can be computed by circuits of AND gates and OR...

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Residue number system

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of modular values. The arithmetic of a residue numeral system is also called multi-modular arithmetic. Multi-modular arithmetic is widely used for computation...

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Logic gate

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can be described with Boolean logic. Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory,...

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Descriptive complexity theory

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Descriptive complexity is a branch of computational complexity theory and of finite model theory that characterizes complexity classes by the type of logic...

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Integer circuit

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In computational complexity theory, an integer circuit is a circuit model of computation in which inputs to the circuit are sets of integers and each gate...

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Descriptive Complexity

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arithmetic, the BIT predicate, and the notion of a first-order query) and complexity theory (including formal languages, resource-bounded complexity classes...

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Central processing unit

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electronic circuitry executes instructions of a computer program, such as arithmetic, logic, controlling, and input/output (I/O) operations. This role contrasts...

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