Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circuit Evaluation for Finite Semirings   The computational complexity of the circuit evaluation problem for finite
semirings is considered, where semirings are not assumed to have an additive or
multiplicative identity. The following dichotomy is shown: If a finite semiring
is such that (i) the multiplicative semigroup is solvable and (ii) it does not
contain a subsemiring with an additive identity $0$ and a multiplicative
identity $1 \neq 0$, then the circuit evaluation problem for the semiring is in
$\mathsf{DET} \subseteq \mathsf{NC}^2$. In all other cases, the circuit
evaluation problem is $\mathsf{P}$-complete.

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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph