Questions tagged [arithmetic-circuits]

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Generalizations of the determinant/permanent problem?

A tantalizing open question in computational complexity is to understand the 'behavioral differences' between the determinant and the permanent. While the former is computable in polynomial time with ...
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Tribes function vs (modified) polynomial threshold circuits

Are there lowerbounds known for representing the Tribes function by a circuit consisting of a single layer of polynomial threshold gates feeding into maybe a trivial summing gate? (Even for degree $1$ ...
337 views

intuition that VP=?VNP is (not?) connected to P=?NP

recently there has been major progress into the VP=?VNP problem for algebraic circuits originated by Valiant, inspiring some optimistic outlook on its eventual or imminent resolution.[1] what is an ...
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Number of composite factors as a function of the number of bits of an integer

Is there a standard formula to calculate the number of composite factors using the number of bits of an integer?
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Arithmetic complexity of matrix powering with non-commutative entries

Assume $M\in\Bbb Z_{\geq0}[x_1,\dots,x_n]^{m\times m}$ be an $m\times m$ matrix in $n$ variables with $x_i$ being non-commutative. What is the complexity class and circuit and formula complexity of ...
How can I transform the term $x>C$ (i.e. the term assumes the value $1$ if $x>C$ and assumes the value $0$ otherwise) to an arithmetic circuit that computes it? Where $x$ is the input to the ...
Consider a function $f : \mathbb R^m \rightarrow \mathbb R^n$. Function $f$ can be written down as a simple arithmetic program. It uses addition, subtraction, multiplication and division - however, ...