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REPORTS > KEYWORD > LOWERBOUNDS:
Reports tagged with lowerbounds:
TR98-036 | 11th June 1998
Vince Grolmusz, Gábor Tardos

#### Lower Bounds for (MOD p -- MOD m) Circuits

Modular gates are known to be immune for the random
restriction techniques of Ajtai; Furst, Saxe, Sipser; and Yao and
Hastad. We demonstrate here a random clustering technique which
overcomes this difficulty and is capable to prove generalizations of
several known modular circuit lower bounds of Barrington, Straubing,
Therien; Krause ... more >>>

TR19-170 | 27th November 2019
Prerona Chatterjee, Mrinal Kumar, Adrian She, Ben Lee Volk

#### A Quadratic Lower Bound for Algebraic Branching Programs

Revisions: 3

We show that any Algebraic Branching Program (ABP) computing the polynomial $\sum_{i = 1}^n x_i^n$ has at least $\Omega(n^2)$ vertices. This improves upon the lower bound of $\Omega(n\log n)$, which follows from the classical result of Baur and Strassen [Str73, BS83], and extends the results by Kumar [Kum19], which showed ... more >>>

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