Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Descriptive Complexity of $\#\textrm{AC}^0$ Functions   We introduce a new framework for a descriptive complexity approach to
arithmetic computations. We define a hierarchy of classes based on the idea of
counting assignments to free function variables in first-order formulae. We
completely determine the inclusion structure and show that #P and #AC^0 appear
as classes of this hierarchy. In this way, we unconditionally place #AC^0
properly in a strict hierarchy of arithmetic classes within #P. We compare our
classes with a hierarchy within #P defined in a model-theoretic way by Saluja
et al. We argue that our approach is better suited to study arithmetic circuit
classes such as #AC^0 which can be descriptively characterized as a class in
our framework.

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The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math