Difference between revisions of "Complexity Zoo:X"
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| − | ===== <span id="xormipstar21" style="color:red">XOR-MIP*[2,1]</span>: {{zcls|m| | + | ===== <span id="xormipstar21" style="color:red">XOR-MIP*[2,1]</span>: {{zcls|m|mipstar|MIP*[2,1]}} With 1-Bit Proofs ===== |
| − | Same as | + | Same as {{zcls|m|mipstar|MIP*[2,1]}}, but with the further restriction that both provers send only a single bit to the verifier, and the verifier's output is a function of the exclusive-OR of those bits. There should exist 0<''a''<''b''<1 such that if the answer is "yes", then for some responses of the provers the verifier accepts with probability at least ''b'', while if the answer is "no", then for all responses of the provers the verifier accepts with probability at most ''a''. |
Defined by [[zooref#cht04|[CHT+04]]], whose motivation was a connection to the Bell and CHSH inequalities of quantum physics. | Defined by [[zooref#cht04|[CHT+04]]], whose motivation was a connection to the Bell and CHSH inequalities of quantum physics. | ||
Revision as of 14:11, 20 June 2013
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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
XOR-MIP*[2,1] - XL - XNL - XP - XPuniform
XOR-MIP*[2,1]: MIP*[2,1] With 1-Bit Proofs
Same as MIP*[2,1], but with the further restriction that both provers send only a single bit to the verifier, and the verifier's output is a function of the exclusive-OR of those bits. There should exist 0<a<b<1 such that if the answer is "yes", then for some responses of the provers the verifier accepts with probability at least b, while if the answer is "no", then for all responses of the provers the verifier accepts with probability at most a.
Defined by [CHT+04], whose motivation was a connection to the Bell and CHSH inequalities of quantum physics.
XOR-MIP*[2,1] is contained in NEXP [CHT+04].
XOR-MIP*[2,1] is contained in QIP[2] [Weh06]
XP: Fixed-Parameter Tractable for Each Parameter
The class of decision problems of the form (x,k) (k a parameter) that are solvable in time O(|x|f(k)) for some function f. The algorithm used may depend on k.
Defined in [DF99].
Contains XPuniform.
Strictly contains FPT (by diagonalization).
XPuniform: Uniform XP
Same as XP except that the algorithm used must be the same for each k (though it can take k as input).
Defined in [DF99].