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  • 1.
    Chattopadhyay, Arkadev
    et al.
    Tata Institute of Fundamental Research, Mumbai, Mumbai, India.
    Koucký, Michal
    Charles University, Prague Praha, Czech Republic.
    Loff, Bruno
    INESC-TEC & U. Porto, Porto, Portugal.
    Mukhopadhyay, Sagnik
    KTH, School of Electrical Engineering and Computer Science (EECS), Theoretical Computer Science, TCS.
    Simulation Theorems via Pseudo-random Properties2019In: Computational Complexity, ISSN 1016-3328, E-ISSN 1420-8954, Vol. 28, no 4, p. 617-659Article in journal (Refereed)
    Abstract [en]

    We generalize the deterministic simulation theorem of Raz & McKenzie (Combinatorica 19(3):403–435, 1999), to any gadget which satisfies a certainhitting property. We prove that inner product and gap-Hammingsatisfy this property, and as a corollary, we obtain a deterministic simulationtheorem for these gadgets, where the gadget’s input size is logarithmicin the input size of the outer function. This yields the firstdeterministic simulation theorem with a logarithmic gadget size, answeringan open question posed by Göös, Pitassi & Watson (in: Proceedingsof the 56th FOCS, 2015). Our result also implies the previous results for the indexing gadget, withbetter parameters than was previously known. Moreover, a simulationtheorem with logarithmic-sized gadget implies a quadratic separationin the deterministic communication complexity and the logarithm ofthe 1-partition number, no matter how high the 1-partition number iswith respect to the input size—something which is not achievable by previous results of Göös, Pitassi & Watson (2015).

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