Difference between revisions of "Complexity Zoo:Y"
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| + | ===== <span id="yp*" style="color:red">YP*</span>: Yaroslav-Percival Star ===== | ||
| + | [[Complexity Zoo:Y#yp|YP]] except the advice string s_n can be verified in polynomial time without needing the input x [[zooref#AD14|[AD14]]]. | ||
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| + | ---- | ||
===== <span id="ypp" style="color:red">YPP</span>: Yaroslav [[Complexity Zoo:B#bpp|BPP]] ===== | ===== <span id="ypp" style="color:red">YPP</span>: Yaroslav [[Complexity Zoo:B#bpp|BPP]] ===== | ||
The probabilistic analogue of [[#yp|YP]]; it is to YP what [[Complexity Zoo:M#ma|MA]] is to [[Complexity Zoo:N#np|NP]]. Formally, the class of decision problems for which there exists a syntactic [[Complexity Zoo:B#bpp|BPP]] machine M such that: | The probabilistic analogue of [[#yp|YP]]; it is to YP what [[Complexity Zoo:M#ma|MA]] is to [[Complexity Zoo:N#np|NP]]. Formally, the class of decision problems for which there exists a syntactic [[Complexity Zoo:B#bpp|BPP]] machine M such that: | ||
Revision as of 10:13, 15 March 2024
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Lists of related classes: Communication Complexity - Hierarchies - Nonuniform
YACC: Yet Another Complexity Class
A term of derision, used against a complexity class.
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 sn such that M(x,sn) 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.
YP*: Yaroslav-Percival Star
YP except the advice string s_n can be verified in polynomial time without needing the input x [AD14].
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 an such that for all inputs x of size n, M(x,an) 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.
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.