Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Feasible combinatorial matrix theory   We show that the well-known Konig's Min-Max Theorem (KMM), a fundamental
result in combinatorial matrix theory, can be proven in the first order theory
$\LA$ with induction restricted to $\Sigma_1^B$ formulas. This is an
improvement over the standard textbook proof of KMM which requires $\Pi_2^B$
induction, and hence does not yield feasible proofs --- while our new approach
does. $\LA$ is a weak theory that essentially captures the ring properties of
matrices; however, equipped with $\Sigma_1^B$ induction $\LA$ is capable of
proving KMM, and a host of other combinatorial properties such as Menger's,
Hall's and Dilworth's Theorems. Therefore, our result formalizes Min-Max type
of reasoning within a feasible framework.

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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
16
The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex