  Non-signaling strategies are a generalization of quantum strategies that have
been studied in physics over the past three decades. Recently, they have found
applications in theoretical computer science, including to proving
inapproximability results for linear programming and to constructing protocols
for delegating computation. A central tool for these applications is
probabilistically checkable proof (PCPs) systems that are sound against
non-signaling strategies.
  In this paper we show, assuming a certain geometrical hypothesis about noise
robustness of non-signaling proofs (or, equivalently, about robustness to noise
of solutions to the Sherali-Adams linear program), that a slight variant of the
parallel repetition of the exponential-length constant-query PCP construction
due to Arora et al. (JACM 1998) is sound against non-signaling strategies with
constant locality.
  Our proof relies on the analysis of the linearity test and agreement test
(also known as the direct product test) in the non-signaling setting.
