Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ptarithmetic   The present article introduces ptarithmetic (short for "polynomial time
arithmetic") -- a formal number theory similar to the well known Peano
arithmetic, but based on the recently born computability logic (see
http://www.cis.upenn.edu/~giorgi/cl.html) instead of classical logic. The
formulas of ptarithmetic represent interactive computational problems rather
than just true/false statements, and their "truth" is understood as existence
of a polynomial time solution. The system of ptarithmetic elaborated in this
article is shown to be sound and complete. Sound in the sense that every
theorem T of the system represents an interactive number-theoretic
computational problem with a polynomial time solution and, furthermore, such a
solution can be effectively extracted from a proof of T. And complete in the
sense that every interactive number-theoretic problem with a polynomial time
solution is represented by some theorem T of the system.
  The paper is self-contained, and can be read without any previous familiarity
with computability logic.

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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph