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Limit, Logic, and Computation

Michael H. Freedman
Proceedings of the National Academy of Sciences of the United States of America
Vol. 95, No. 1 (Jan. 6, 1998), pp. 95-97
Stable URL: http://www.jstor.org/stable/44421
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Limit, Logic, and Computation
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Abstract

We introduce ``ultrafilter limits'' into the classical Turing model of computation and develop a paradigm for interpreting the problem of distinguishing the class P from NP as a logical problem of decidability. We use P(NP) to denote decision problems which can be solved on a (nondeterministic) Turing machine in polynomial time. The concept is that in an appropriate limit it may be possible to prove that problems in P are still decidable, so a problem whose limit is undecidable would be established as lying outside of P.

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