Kapron, B. M., and Cook, S. A. (1996), A new characterization of type-2 feasibility, SIAM J. Computing 25, 117--132.  Home/Search   Document Not in Database   Summary   Related Articles

....to define a type 2 relation (or function) in which the oracle is one of the arguments of the relation. For the case of polynomial time, where the oracle represents a function whose growth affects the input size, this point of view was taken by Constable [5] and Mehlhorn [20] see also [18] and [17]) For the case of the polynomial hierarchy, where the oracle represents a function whose growth does not affect the input size, this point of view was taken by Townsend [27] see also [28] and [29] For the case of NP search classes, this was done by Beame et al. [2] Baker, Gill, and Solovay ....

....convenient to allow a function argument ff : Sigma Gamma Sigma in a relation R( x; ff) in place of a set argument X. Townsend [27] defined a type 2 version of the polynomial hierarchy based on this idea (see also [28, 29] We follow Townsend (in contrast to Mehlhorn [20] see also [5] [17] and [12] in ignoring the oracle ff in allotting time to a Turing machine with oracle ff. That is, we say that a Turing machine M with oracle ff which computes R( x; ff) is T (n) time bounded provided that for all x and for all ff, M halts within T (n) steps, where n is the length of x. In ....

Kapron, B. M., and Cook, S. A. (1996), A new characterization of type-2 feasibility, SIAM J. Computing 25, 117--132.

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