J. Royer, Semantics versus syntax versus computations: Machine models for type-2 polynomial-time bounded functionals, Journal of Computer and System Science 54 (1997), 424--436. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
On Characterizations of the Basic Feasible Functionals, Part I - Irwin, Kapron, Royer (2001) (1 citation) Self-citation (Royer) (Correct)
....inputs compute exactly the type 2 BFFs. These notions are treated in Section 6. Seth [Set95] extended Kapron and Cook s argument to give a machine characterization of the BFFs at all simple types. Seth s characterization is treated at some length in this paper s sequel. In related work, Royer [Roy97] showed that BFF 2 satisfies a weak analogue of the Kreisel Lacombe Shoenfield Theorem [KLS57] While the evidence is still incomplete, BFF 2 has proven to be a strong candidate for the natural type 2 analogue of PF. For the BFFs at type 3 and above the situation is much less clear, as discussed ....
.... of care in the construction of the M i,d,k s, one can arrange that there is a k 0 such that, for all i, d, k, and x, at any time in the computation, the run time of M i,d,k on input (f, x) up to that point is bounded by q d,k ( # , x ) q d 1,k0 ( # , k x ) Seth [Set92] and Royer [Roy97] provide for details on similar clocking schemes. Thus by Lemma 12, M i,d,k computes a basic polynomial time functional. If M i is an OTM that just happens to run within a q d,k time bound, then it follows from the construction and Lemma 12 that M i and M i,d,k compute the same functional. ....
J. Royer, Semantics versus syntax versus computations: Machine models for type-2 polynomial-time bounded functionals, Journal of Computer and System Science 54 (1997), 424--436.
On Characterizations of the Basic Feasible Functionals, Part I - Irwin, Kapron, Royer (1999) (1 citation) Self-citation (Royer) (Correct)
....inputs compute exactly the type 2 BFFs. These notions are treated in Section 6. Seth [Set95] extended Kapron and Cook s argument to give a machine characterization of the BFFs at all simple types. Seth s characterization is treated at some length in this paper s sequel. In related work, Royer [Roy97] showed that BFF 2 satisfies a weak analogue of the Kreisel Lacombe Shoenfield Theorem [KLS57] While the evidence is still incomplete, BFF 2 has proven to be a strong candidate for the natural type 2 analogue of PF. For the BFFs at type 3 and above the situation is much less clear, as discussed ....
.... there is a k 0 such that, for all i, d, k, and x, at any time in the computation, the run time of M i,d,k on input (f, x) up to that point is bounded by 21 July 1999 On Characterizations of the BFFs, Part I Draft 19 q d,k ( # , x ) q d 1,k0 ( # , k x ) Seth [Set92] and Royer [Roy97] provide for details on similar clocking schemes. Thus by Lemma 12, M i,d,k computes a basic polynomial time functional. If M i is an OTM that just happens to run within a q d,k time bound, then it follows from the construction and Lemma 12 that M i and M i,d,k compute the same functional. ....
J. Royer, Semantics versus syntax versus computations: Machine models for type-2 polynomial-time bounded functionals, Journal of Computer and System Science 54 (1997), 424--436.
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