Computational complexity theory

study of a model of computation

theoretical computer science and mathematics theory that classifies problems according to their inherent difficulty, and relates those classes to each other

estimate of time taken for running an algorithm

study of resources used by an algorithm

measure of algorithmic complexity

set of problems in computational complexity theory of related resource-based complexity

sufficient evidence or a sufficient argument for the truth of a proposition

mathematical model describing how an output of a function is computed given an input

measure of the amount of resources needed to run an algorithm or solve a computational problem

class of algorithms that find approximate solutions to optimization problems

potential ability of quantum computing devices to solve problems efficiently that classical computers practically cannot solve efficiently

subset of mathematical optimization

Term in Complexity Theory

model in computer science

amount of memory space that an algorithm uses as a function of the input's size

measure of how efficiently algorithms use resources

in computational complexity theory, an abstract machine modeling computation as two parties (an untrusted but powerful ‘prover’; a trusted ‘verifier’ with bounded resources) exchanging messages to ascertain whether some string belongs to a language

model of computation

computational problem of determining whether two finite graphs are isomorphic

complexity of sending information in a distributed algorithm

computational complexity of quantum algorithms

selection of a hash function at random from a family of hash functions with a certain mathematical property, guaranteeing a low number of collisions in expectation, even if the data is chosen by an adversary

era of technology characterized by quantum processors with <1000 qubits sensitive to noise, prone to quantum decoherence, and incapable of continuous quantum error correction

relating to decision problems and complexity classes

L-notation is an asymptotic notation analogous to big-O notation, denoted as L_n[\alpha,c] for a bound variable n tending to infinity. Like big-O notation, it is usually used to roughly convey the rate of growth of a function, such as the computational complexity of a particular algorithm.

branch of computational complexity theory

abstraction in a computational model describing a kind of computer resource an algorithm uses

notion of the "hardest" or "most general" problem in a complexity class

Quantum algorithm

model of computational complexity

problem whose solution requires a computer at least the size of the Earth and a time period at least the estimated age of the Earth to be computed

subfield of topology with an overlap with areas of computer science

model of computational complexity

algorithmic runtime requirements for common math procedures

type of formal language in computational complexity theory

branch of mathematical logic

Complexity measure in computer science

equivalence of average-case and expected complexity

function whose values can be computed in a number of steps or a number of Turing-machine cells of order given by the function itself

computational complexity as measured by the limiting behavior of resource usage for large inputs

property of computational problems that is a special case of NP-completeness

formal language in computational complexity theory

graph Machine

hypothesis in computational complexity theory