Consistency and optimality

Authors:
Yijia Chen;Jörg Flum;Moritz Müller
Affiliations:
Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;Abteilung für Mathematische Logik, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany;Centre de Recerca Matemàtica, Bellaterra, Spain
Venue:
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Year:
2011

Citing 3
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Abstract

Assume that the problem Q0 is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T ∪{ConT} as the minimal extension of T proving for some algorithm that it decides Q0 as fast as any algorithm B with the property that T proves that B decides Q0. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.