Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak length induction and slow growing depth boolean circuits   We define a hierarchy of circuit complexity classes LD^i, whose depth are the
inverse of a function in Ackermann hierarchy. Then we introduce extremely weak
versions of length induction and construct a bounded arithmetic theory L^i_2
whose provably total functions exactly correspond to functions computable by
LD^i circuits. Finally, we prove a non-conservation result between L^i_2 and a
weaker theory AC^0CA which corresponds to the class AC^0. Our proof utilizes
KPT witnessing theorem.

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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: math
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an