Computational Flows in Arithmetic
release_aigaig7vw5fvjdfm7iyc2ybni4
by
Amirhossein Akbar Tabatabai
2017
Abstract
A computational flow is a pair consisting of a sequence of computational
problems of a certain sort and a sequence of computational reductions among
them. In this paper we will develop a theory for these computational flows and
we will use it to make a sound and complete interpretation for bounded theories
of arithmetic. This property helps us to decompose a first order arithmetical
proof to a sequence of computational reductions by which we can extract the
computational content of low complexity statements in some bounded theories of
arithmetic such as IΔ_0, T^k_n, IΔ_0+EXP and PRA. In the last
section, by generalizing term-length flows to ordinal-length flows, we will
extend our investigation from bounded theories to strong unbounded ones such as
IΣ_n and PA+TI(α) and we will capture their total NP search
problems as a consequence.
In text/plain
format
Archived Files and Locations
application/pdf 316.6 kB
file_o2a7q7o5brbkbmngnrtb35thvm
|
arxiv.org (repository) web.archive.org (webarchive) |
1711.01735v1
access all versions, variants, and formats of this works (eg, pre-prints)