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On Proving Parameterized Size Lower Bounds for Multilinear Algebraic Models

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Języki publikacji
EN
Abstrakty
EN
We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ(t(k)) lower bound for some function t of k ) on the size of the above models computing a multilinear polynomial that can be computed by a depth four circuit of size g (k)n0(1) for some computable function g. Further, we obtain a parameterized separation between ROABPs and read-2 ABPs. This is obtained by constructing a degree k polynomial that can be computed by a read-2 ABP of small size such that the rank of the partial derivative matrix under any partition of the variables is large.
Wydawca
Rocznik
Strony
69--93
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
  • Indian Institute of Technology, Madras, Chennai 600036, India
  • Indian Institute of Technology, Madras, Chennai 600036, India
Bibliografia
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  • [5] Grochow JA, Mulmuley KD, Qiao Y. Boundaries of VP and VNP. In: Chatzigiannakis I, Mitzenmacher M, Rabani Y, Sangiorgi D (eds.), 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, volume 55 of LIPIcs. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016 pp. 34:1-34:14. doi:10.4230/LIPIcs.ICALP.2016.34.
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-1474e5de-cf45-4ade-beb6-7f24b6f8de5d
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