Simulation Theorems via Pseudorandom Properties
Computational Complexity
2017-04-25 v1
Abstract
We generalize the deterministic simulation theorem of Raz and McKenzie [RM99], to any gadget which satisfies certain hitting property. We prove that inner-product and gap-Hamming satisfy this property, and as a corollary we obtain deterministic simulation theorem for these gadgets, where the gadget's input-size is logarithmic in the input-size of the outer function. This answers an open question posed by G\"{o}\"{o}s, Pitassi and Watson [GPW15]. Our result also implies the previous results for the Indexing gadget, with better parameters than was previously known. A preliminary version of the results obtained in this work appeared in [CKL+17].
Keywords
Cite
@article{arxiv.1704.06807,
title = {Simulation Theorems via Pseudorandom Properties},
author = {Arkadev Chattopadhyay and Michal Koucký and Bruno Loff and Sagnik Mukhopadhyay},
journal= {arXiv preprint arXiv:1704.06807},
year = {2017}
}