2-Local Random Reductions to 3-Valued Functions

Abstract

Yao (in a lecture at DIMACS Workshop on structural complexity and cryptography, 1990) showed that if a language L is 2-locally random reducible to a Boolean function, then L ∈ PSPACE/poly. Fortnow & Szegedy quantitatively improved Yao’s result to show that such languages are in fact in NP/poly (Information Processing Letters, 1992). In this paper we extend Yao’s result to show that if a language L is 2-locally random reducible to a target function which takes values in {0, 1, 2}, then L ∈ PSPACE/poly.