Abstract
Assume that the problem Q 0 is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T ∪ {Con T } as the minimal extension of T proving for some algorithm that it decides Q 0 as fast as any algorithm \(\mathbb B\) with the property that T proves that \(\mathbb B\) decides Q 0. Here, Con T claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.
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Chen, Y., Flum, J., Müller, M. (2011). Consistency and Optimality. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_7
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DOI: https://doi.org/10.1007/978-3-642-21875-0_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21874-3
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