Speedup for Natural Problems and Noncomputability
Computational Complexity
2012-09-24 v3
Abstract
A resource-bounded version of the statement "no algorithm recognizes all non-halting Turing machines" is equivalent to an infinitely often (i.o.) superpolynomial speedup for the time required to accept any coNP-complete language and also equivalent to a superpolynomial speedup in proof length in propositional proof systems for tautologies, each of which implies P!=NP. This suggests a correspondence between the properties 'has no algorithm at all' and 'has no best algorithm' which seems relevant to open problems in computational and proof complexity.
Cite
@article{arxiv.0906.3765,
title = {Speedup for Natural Problems and Noncomputability},
author = {Hunter Monroe},
journal= {arXiv preprint arXiv:0906.3765},
year = {2012}
}
Comments
8 pages