Abstract
For each n, we give weak theories of bounded arithmetic, whose provably recursive functions (having appropriate graphs) are exactly those functions computable deterministically in n-fold time TIME(2(n,p(|x|))), where p is a polynomial and 2(n,z) is a stack of n two's topped by a z. In proving this result, we separate out the time contribution due to different variables in a multivariate function. These results further the evidence that “normalized” formal logic proofs (free cut free proof in Gentzen sequent calculus) of the totality of a function furnish an algorithm to compute the function.
The first author was partially supported by NSF funding while visiting the University of Illinois as well as by a Boston College Summer Research Grant.
The second author was partially supported by NSF Grant DMS 84-21214.
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© 1986 Springer-Verlag Berlin Heidelberg
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Clote, P., Takeuti, G. (1986). Exponential time and bounded arithmetic. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_94
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DOI: https://doi.org/10.1007/3-540-16486-3_94
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