Simulation Theorems via Pseudorandom Properties

Arkadev Chattopadhyay; Michal Koucký; Bruno Loff; Sagnik Mukhopadhyay

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arXiv · 1704.06807

Simulation Theorems via Pseudorandom Properties

Arkadev Chattopadhyay·Michal Koucký·Bruno Loff·Sagnik Mukhopadhyay

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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].

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Arkadev Chattopadhyay, Michal Koucký, Bruno Loff, Sagnik Mukhopadhyay. 2017-04-22. Simulation Theorems via Pseudorandom Properties. https://arxiv.org/abs/1704.06807

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