Finding pessiland

Abstract

We explore the minimal assumptions that are necessary for non-trivial argument systems, such as Kilian's argument system for NP with polylogarithmic communication complexity [K92]. We exhibit an oracle relative to which there is a 2-round argument system with poly-logarithmic communication complexity for some language in NP, but no one-way functions. The language lies outside BPTime(20 0(n)), so the relaxation to computational soundness is essential for achieving sublincar communication complexity. We obtain as a corollary that under black-box reductions, non-trivial argument systems do not imply one-way functions. © Springer-Verlag Berlin Heidelberg 2006.