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Electronic Colloquium on Computational Complexity

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Reports tagged with lower bound for circuit size:
TR14-139 | 31st October 2014
Hong Van Le

Lower bounds for the circuit size of partially homogeneous polynomials

Revisions: 1

In this paper
we associate to each multivariate polynomial $f$ that is homogeneous relative to a subset of its variables a series of polynomial families $P_\lambda (f)$ of $m$-tuples of homogeneous polynomials of equal degree such that the circuit size of any member in $P_\lambda (f)$ is bounded from above ... more >>>

TR17-124 | 6th August 2017
Mrinal Kumar, Ben Lee Volk

An Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

Revisions: 2

We prove a lower bound of $\Omega(n^2/\log^2 n)$ on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial $f(x_1, \ldots, x_n)$. Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff [RSY08], who proved a lower bound of $\Omega(n^{4/3}/\log^2 n)$ for the same ... more >>>

TR19-047 | 2nd April 2019
Mrinal Kumar, Ben Lee Volk

Lower Bounds for Matrix Factorization

We study the problem of constructing explicit families of matrices which cannot be expressed as a product of a few sparse matrices. In addition to being a natural mathematical question on its own, this problem appears in various incarnations in computer science; the most significant being in the context of ... more >>>

TR20-033 | 12th March 2020
Suryajith Chillara

New Exponential Size Lower Bounds against Depth Four Circuits of Bounded Individual Degree

Revisions: 1

Kayal, Saha and Tavenas [Theory of Computing, 2018] showed that for all large enough integers $n$ and $d$ such that $d\geq \omega(\log{n})$, any syntactic depth four circuit of bounded individual degree $\delta = o(d)$ that computes the Iterated Matrix Multiplication polynomial ($IMM_{n,d}$) must have size $n^{\Omega\left(\sqrt{d/\delta}\right)}$. Unfortunately, this bound ... more >>>

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