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Simulation Theorems via Pseudo-random Properties
Tata Institute of Fundamental Research, Mumbai, Mumbai, India.
Charles University, Prague Praha, Czech Republic.
INESC-TEC & U. Porto, Porto, Portugal.
KTH, Skolan för elektroteknik och datavetenskap (EECS), Teoretisk datalogi, TCS.
2019 (engelsk)Inngår i: Computational Complexity, ISSN 1016-3328, E-ISSN 1420-8954, Vol. 28, nr 4, s. 617-659Artikkel i tidsskrift (Fagfellevurdert) Published
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).

sted, utgiver, år, opplag, sider
Springer, 2019. Vol. 28, nr 4, s. 617-659
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URN: urn:nbn:se:kth:diva-258086DOI: 10.1007/s00037-019-00190-7ISI: 000491059300003Scopus ID: 2-s2.0-85069433764OAI: oai:DiVA.org:kth-258086DiVA, id: diva2:1349765
Merknad

QC 20191008. QC 20191106

Tilgjengelig fra: 2019-09-09 Laget: 2019-09-09 Sist oppdatert: 2019-11-06bibliografisk kontrollert

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