Complexity Zoo:Y

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Complexity classes by letter: Symbols - A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

Lists of related classes: Communication Complexity - Hierarchies - Nonuniform

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YACC - YP - YPP - YQP

YACC: Yet Another Complexity Class

A term of derision, used against a complexity class.

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YP: Your Polynomial-Time or Yaroslav-Percival

The class of decision problems for which there exists a polynomial-time machine M such that:

• For all input sizes n, there exists a polynomial-size advice string s_n such that M(x,s_n) outputs the correct answer for all inputs x of size n.
• For all inputs x and advice strings s, M(x,s) outputs either the correct answer or "I don't know."

Defined in a recent post of the blog Shtetl-Optimized. See there for an explanation of the class's name.

Contains ZPP by the same argument that places BPP in P/poly.

Also contains P with TALLY ∩ NP ∩ coNP oracle.

Is contained in NP ∩ coNP and YPP.

Is equal to ONP ∩ coONP.

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YP*: Yaroslav-Percival Star

YP except the advice string s_n can be verified in polynomial time without needing the input x [AD14].

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YPP: Yaroslav BPP

The probabilistic analogue of YP; it is to YP what MA is to NP. Formally, the class of decision problems for which there exists a syntactic BPP machine M such that:

• For all input sizes n, there exists a polynomial-size advice string a_n such that for all inputs x of size n, M(x,a_n) outputs the correct answer with probability at least 2/3.
• For all inputs x and advice strings a, the probability that M(x,a) outputs the incorrect answer is at most 1/3. In other words, the sum of the probabilities of the correct answer and "I don't know" is at least 2/3.

To amplify a YPP machine, one can run it multiple times, then accept if a majority of runs accept, reject if a majority reject, and otherwise output "I don't know."

Contains BPP and YP, and is contained in MA and P/poly.

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YQP: Yaroslav BQP

Is to YPP as BQP is to BPP, and QMA is to MA. The machine is now a quantum computer and the advice is a quantum state |ψ_n>.

Contains BQP and YPP, and is contained in QMA and BQP/qpoly.

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YQP*: Yaroslav BQP star

Is to YQP as YP* is to YP [AD14].

Is contained in APP, and so is low for PP [Yir24].

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YQP*/poly: YQP* With Polynomial-Size Advice

Equal to BQP/qpoly [AD14].

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