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What (who) is ZPP (complexity) - definition

COMPLEXITY CLASS

Zero error probability in polynomial time; Zero-error Probabilistic Polynomial time

ZPP (complexity)

In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists with these properties:

https://en.wikipedia.org/wiki/ZPP_(complexity)

Computational complexity

MEASURE OF THE AMOUNT OF RESOURCES NEEDED TO RUN AN ALGORITHM OR SOLVE A COMPUTATIONAL PROBLEM

Asymptotic complexity; Computational Complexity; Bit complexity; Context of computational complexity; Complexity of computation (bit); Computational complexities

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements.

https://en.wikipedia.org/wiki/Computational_complexity

complexity

PROFESSIONAL ESPORTS ORGANIZATION BASED IN THE UNITED STATES

Los Angeles Complexity; CompLexity Gaming; LA Complexity; Complexity LA; CompLexity; Team CompLexity; CoL.Black; CoL

<algorithm> The level in difficulty in solving mathematically posed problems as measured by the time, number of steps or arithmetic operations, or memory space required (called time complexity, computational complexity, and space complexity, respectively). The interesting aspect is usually how complexity scales with the size of the input (the "scalability"), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N). See also NP-complete. (1994-10-20)

Wikipedia

ZPP (complexity)

In complexity theory, ZPP (zero-error probabilistic polynomial time) is the complexity class of problems for which a probabilistic Turing machine exists with these properties:

It always returns the correct YES or NO answer.
The running time is polynomial in expectation for every input.

In other words, if the algorithm is allowed to flip a truly-random coin while it is running, it will always return the correct answer and, for a problem of size n, there is some polynomial p(n) such that the average running time will be less than p(n), even though it might occasionally be much longer. Such an algorithm is called a Las Vegas algorithm.

Alternatively, ZPP can be defined as the class of problems for which a probabilistic Turing machine exists with these properties:

It always runs in polynomial time.
It returns an answer YES, NO or DO NOT KNOW.
The answer is always either DO NOT KNOW or the correct answer.
It returns DO NOT KNOW with probability at most 1/2 for every input (and the correct answer otherwise).

The two definitions are equivalent.

The definition of ZPP is based on probabilistic Turing machines, but, for clarity, note that other complexity classes based on them include BPP and RP. The class BQP is based on another machine with randomness: the quantum computer.

https://en.wikipedia.org/wiki/ZPP (complexity)