| Cook, S. and, Urquhart, A. (1993) Functional interpretaions of feasibly constructive arithmetic, Annals of Pure and Applied Logic 63, 103--200. |
....greatest common divisors, when the input polynomials are accessed only through queries. Another example is NP search problems, where the input is an exponentially large search space. Beame et al. [2] give a natural type 2 description of such problems. For a third example, Cook and Urquhart [7] show how to use higher type polynomial time functions to give constructive meaning to number theory theorems proved in a certain formal system. An oracle Turing machine (OTM) is a Turing machine that is able to make queries at unit cost to its oracle , representing a set or function. Such ....
Cook, S. and, Urquhart, A. (1993) Functional interpretaions of feasibly constructive arithmetic, Annals of Pure and Applied Logic 63, 103--200.
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