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Electronic Colloquium on Computational Complexity

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Reports tagged with circuit lower bound:
TR11-086 | 2nd June 2011
Masaki Yamamoto

A tighter lower bound on the circuit size of the hardest Boolean functions

In [IPL2005],
Frandsen and Miltersen improved bounds on the circuit size $L(n)$ of the hardest Boolean function on $n$ input bits:
for some constant $c>0$:
\left(1+\frac{\log n}{n}-\frac{c}{n}\right)
\left(1+3\frac{\log n}{n}+\frac{c}{n}\right)
In this note,
we announce a modest ... more >>>

TR12-071 | 29th May 2012
Kazuhisa Seto, Suguru Tamaki

A Satisfiability Algorithm and Average-Case Hardness for Formulas over the Full Binary Basis

We present a moderately exponential time algorithm for the satisfiability of Boolean formulas over the full binary basis.
For formulas of size at most $cn$, our algorithm runs in time $2^{(1-\mu_c)n}$ for some constant $\mu_c>0$.
As a byproduct of the running time analysis of our algorithm,
we get strong ... more >>>

TR16-085 | 28th May 2016
Shiteng Chen, Periklis Papakonstantinou

Depth-reduction for composites

We obtain a new depth-reduction construction, which implies a super-exponential improvement in the depth lower bound separating $NEXP$ from non-uniform $ACC$.

In particular, we show that every circuit with $AND,OR,NOT$, and $MOD_m$ gates, $m\in\mathbb{Z}^+$, of polynomial size and depth $d$ can be reduced to a depth-$2$, $SYM\circ AND$, circuit of ... more >>>

TR16-100 | 27th June 2016
Suguru Tamaki

A Satisfiability Algorithm for Depth Two Circuits with a Sub-Quadratic Number of Symmetric and Threshold Gates

We consider depth 2 unbounded fan-in circuits with symmetric and linear threshold gates. We present a deterministic algorithm that, given such a circuit with $n$ variables and $m$ gates, counts the number of satisfying assignments in time $2^{n-\Omega\left(\left(\frac{n}{\sqrt{m} \cdot \poly(\log n)}\right)^a\right)}$ for some constant $a>0$. Our algorithm runs in time ... more >>>

TR18-188 | 7th November 2018
Zeev Dvir, Alexander Golovnev, Omri Weinstein

Static Data Structure Lower Bounds Imply Rigidity

Revisions: 2

We show that static data structure lower bounds in the group (linear) model imply semi-explicit lower bounds on matrix rigidity. In particular, we prove that an explicit lower bound of $t \geq \omega(\log^2 n)$ on the cell-probe complexity of linear data structures in the group model, even against arbitrarily small ... more >>>

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