Probabilistic Turing machineIn theoretical computer science, a probabilistic Turing machine is a non-deterministic Turing machine that chooses between the available transitions at each point according to some probability distribution.
PostBQPIn computational complexity theory, PostBQP is a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum Turing machine with postselection and bounded error (in the sense that the algorithm is correct at least 2/3 of the time on all inputs).
Low (complexity)In computational complexity theory, a languageB (or a complexity classB) is said to be low for a complexity class A (with some reasonable relativized version of A) if A = A; that is, A with an oracle for B is equal to A. Such a statement implies that an abstract machine that solves problems in A achieves no additional power if it is given the ability to solve problems in B at unit cost.
QMAQMA, as an abbreviation for Quantum Merlin Arthur, refers to a complexity class in computational complexity theory.
Decision problemIn computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding whether a given natural number is prime. Another example is the problem, "given two numbers x and y, does x evenly divide y?"BPP (complexity)In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all instances. BPP is one of the largest practical classes of problems, meaning most problems of interest in BPP have efficient probabilistic algorithms that can be run quickly on real modern machines.
Computational complexity theoryInherent difficulty of computational problemsIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer and is solvable by mechanical application of mathematical steps, such as an algorithm.
Nondeterministic Turing machineIn theoretical computer science and computational theory, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike the standard, deterministic, Turing machine. NTMs are sometimes used in thought experiments to examine the abilities and limits of computers.PostselectionIn probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event E {\displaystyle E} , the probability of some other event F {\displaystyle F} changes from Pr [ F ] {\textstyle \operatorname {Pr} [F]} to the conditional probability Pr [ F | E ] {\displaystyle \operatorname {Pr} [F\,|\,E]} .
BQPIn computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. It is the quantum analogue to the complexity class BPP.
Chernoff boundExponentially decreasing bounds on tail distributions of random variablesIn probability theory, a Chernoff bound is an exponentially decreasing upper bound on the tail of a random variable based on its moment generating function. The minimum of all such exponential bounds forms the Chernoff or Chernoff-Cramér bound, which may decay faster than exponential (e.g. sub-Gaussian).
Time complexityEstimate of time taken for running an algorithmGraphs of functions commonly used in the analysis of algorithms, showing the number of operations N{\displaystyle N} as the result of input size n{\displaystyle n} for each functionIn theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.*As an Amazon Associate I earn from qualifying purchases.