On the communication complexity of XOR functions

نویسندگان

  • Ashley Montanaro
  • Tobias Osborne
چکیده

An XOR function is a function of the form g(x, y) = f(x ⊕ y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we completely characterise one-way communication complexity for all f . We also show that, when f is monotone, g’s quantum and classical complexities are quadratically related, and that when f is a linear threshold function, g’s quantum complexity is Θ(n). More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical exact communication complexities of all XOR functions are asymptotically equivalent. We give two randomised classical protocols for general XOR functions which are efficient for certain functions, and a third protocol for linear threshold functions with high margin. These protocols operate in the symmetric message passing model with shared randomness.

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عنوان ژورنال:
  • CoRR

دوره abs/0909.3392  شماره 

صفحات  -

تاریخ انتشار 2009