Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds for the Size of Nondeterministic Circuits   Nondeterministic circuits are a nondeterministic computation model in circuit
complexity theory. In this paper, we prove a $3(n-1)$ lower bound for the size
of nondeterministic $U_2$-circuits computing the parity function. It is known
that the minimum size of (deterministic) $U_2$-circuits computing the parity
function exactly equals $3(n-1)$. Thus, our result means that nondeterministic
computation is useless to compute the parity function by $U_2$-circuits and
cannot reduce the size from $3(n-1)$. To the best of our knowledge, this is the
first nontrivial lower bound for the size of nondeterministic circuits
(including formulas, constant depth circuits, and so on) with unlimited
nondeterminism for an explicit Boolean function. We also discuss an approach to
proving lower bounds for the size of deterministic circuits via lower bounds
for the size of nondeterministic restricted circuits.

18
The categories of this paper are: econ
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga