Alexander E. Andreev, Andrea E. F. Clementi, Jose Rolim

We prove an optimal bound on the Shannon function

$L(n,m,\epsilon)$ which describes the trade-off between the

circuit-size complexity and the degree of approximation; that is

$$L(n,m,\epsilon)\ =\

\Theta\left(\frac{m\epsilon^2}{\log(2 + m\epsilon^2)}\right)+O(n).$$

Our bound applies to any partial boolean function

and any ...
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Madhu Sudan, Luca Trevisan, Salil Vadhan

Impagliazzo and Wigderson have recently shown that

if there exists a decision problem solvable in time $2^{O(n)}$

and having circuit complexity $2^{\Omega(n)}$

(for all but finitely many $n$) then $\p=\bpp$. This result

is a culmination of a series of works showing

connections between the existence of hard predicates

and ...
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Meena Mahajan, V Vinay

In this note, we consider the problem of computing the

coefficients of the characteristic polynomial of a given

matrix, and the related problem of verifying the

coefficents.

Santha and Tan [CC98] show that verifying the determinant

(the constant term in the characteristic polynomial) is

complete for the class C=L, ...
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Nicola Galesi, Massimo Lauria

We prove that Polynomial Calculus and Polynomial Calculus with Resolution are not automatizable, unless W[P]-hard problems are fixed parameter tractable by one-side error randomized algorithms. This extends to Polynomial Calculus the analogous result obtained for Resolution by Alekhnovich and Razborov (SIAM J. Computing, 38(4), 2008).

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