Similar to NPcc except that the protocol is restricted to have exactly one accepting computation on each yes-input.
The complexity measure corresponding to UPcc is equivalent to the log of the number of rectangles needed to partition the set of 1-entries of the communication matrix.
Introduced in [Yan91], where it was shown that for total functions:
The quadratic overhead in simulating UPcc with Pcc, or equivalently the O(log2(n)) protocol for CISG, is known to be essentially optimal [GPW15].
In a two-party communication complexity problem, Alice and Bob have n-bit strings x and y respectively, and they wish to evaluate some Boolean function f(x,y) using as few bits of communication as possible. Pcc is the class of (infinite families of) f's, such that the amount of communication needed is only O(polylog(n)), even if Alice and Bob are restricted to a deterministic protocol.
Note that all functions of the form above are solvable given bits of communication, since no bounds are placed on the computational abilities of Alice and Bob. Thus, when discussing this class, "polynomially" is sometimes used in place of "polylogarithmically."
Is strictly contained in NPcc and in BPPcc because of the EQUALITY problem.
If the classes are defined in terms of total functions, then Pcc = NPcc ∩ coNPcc = UPcc.
Defined in [BFS86].