A. Cobham. The intrinsic computational di#culty of functions. In Y. BarHillel, editor, Proceedings of the  Home/Search Document Not in Database Summary Related Articles Check |
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Theories With Self-Application and Computational Complexity - Strahm (2001) (Correct)
....collection of projection functions and we simply write # for the 0 ary function being constant to the empty word #. We are now ready to state the function algebra characterizations of the four complexity classes which are relevant in this paper. The characterization of FPtime is due to Cobham [14]. The delineations of FPtimeLinspace and FPspace are due to Thompson [51] Finally, the fourth assertion of our theorem is due to Ritchie [45] For a uniform presentation of all these results we urge the reader to consult Clote [13] 5 Theorem 1 We have the following function algebra ....
Cobham, A. The intrinsic computational di#culty of functions. In Logic, Methodology and Philosophy of Science II. North Holland, Amsterdam, 1965, pp. 24--30.
On Characterizations of the Basic Feasible Functionals, Part II - Irwin, Kapron, Royer (2001) (1 citation) (Correct)
....a justification seem to start with Cobham s 1965 characterization of polynomialtime. Let us o#cially define the polynomial time computable functions (PF) as the class of type level 1 functions computable on deterministic Turing machines within time polynomial in the length of the inputs. Cobham [Cob65] introduced a simple function algebra (let us call it L) and showed that the L computable functions are exactly PF. This characterization provides two analogies to work from in constructing higher type versions of PF: the first being function algebra programming language synthetic side of the ....
.... The first of these three characterizations was through Cook and Kapron s type 2 bounded typed loop programs (abbreviated, BTLP 2 ) programming formalism [CK89, CK90] This is a simply typed, imperative programming formalism with a loop construct based on Cobham s limited recursion on notation [Cob65]. BTLP 2 is representative several restricted programming languages that formalize a type 2 analogue of PF though a careful lift of a programming formalism characterization of PF. Our o#cial definition of BFF 2 was as the BTLP 2 computable functionals. The second characterization considered is ....
A. Cobham, The intrinsic computational di#culty of functions, Proceedings of the International Conference on Logic, Methodology and Philosophy (Y. Bar Hillel, ed.), North-Holland, 1965, pp. 24--30.
On Characterizations of the Basic Feasible Functionals, Part I - Irwin, Kapron, Royer (2001) (1 citation) (Correct)
....is no higher type Church s thesis, even formally posing the problem may itself be di#cult. The emergence of the basic feasible functionals Mehlhorn took up Constable s problem in [Meh74, Meh76] He defined a class of type 2 functionals, denoted L( through a careful relativization of Cobham s [Cob65] syntactic characterization of polynomial time. Cobham s characterization is formally stated as Theorem 2(a) below. Mehlhorn developed some evidence that this class was a type 2 analogue to PF, but his main motivation was to show that L( is a sensible extension of Cook reducibilities to ....
....involved. Cook and Urquhart decided to try to develop a simpler class of realizers for IS 1 2 that could be presented as a feasible variant of Godel s Dialectica interpretation of Heyting Arithmetic [God58, God90] Their approach to this problem was, like Mehlhorn s work, based on Cobham s [Cob65] syntactic definition of polynomial time. Their initial work was independent of Constable and Mehlhorn. They introduced a formal system PV # in which the terms consist of simply typed # expressions built from numeric constants, function constants for each element of PF, variables of all finite ....
[Article contains additional citation context not shown here]
A. Cobham, The intrinsic computational di#culty of functions, Proceedings of the International Conference on Logic, Methodology and Philosophy (Y. Bar Hillel, ed.), North-Holland, 1965, pp. 24--30.
On Characterizations of the Basic Feasible Functionals, Part I - Irwin, Kapron, Royer (1999) (1 citation) (Correct)
....is no higher type Church s thesis, even formally posing the problem may itself be di#cult. The emergence of the basic feasible functionals Mehlhorn took up Constable s problem in [Meh74, Meh76] He defined a class of type 2 functionals, denoted L( through a careful relativization of Cobham s [Cob65] syntactic characterization of polynomial time. Cobham s characterization is formally stated as Theorem 2(a) below. Mehlhorn developed some evidence that this class was a type 2 analogue to PF, but his main motivation was to show that L( is a sensible extension of Cook reducibilities to ....
....involved. Cook and Urquhart decided to try to develop a simpler class of realizers for IS 1 2 that could be presented as a feasible variant of Godel s Dialectica interpretation of Heyting Arithmetic [God58, God90] Their approach to this problem was, like Mehlhorn s work, based on Cobham s [Cob65] syntactic definition of polynomial time. Their initial work was independent of Constable and Mehlhorn. They introduced a 1 Suppose M0 and M1 are two models of computation with associated cost models. M0 and M1 are called polynomially related if and only if there exist a polynomial q and t0 , ....
[Article contains additional citation context not shown here]
A. Cobham, The intrinsic computational di#culty of functions, Proceedings of the International Conference on Logic, Methodology and Philosophy (Y. Bar Hillel, ed.), North-Holland, 1965, pp. 24--30.
On the Expressive Power of Existential Quantification in.. - Spreen (Correct)
.... x denotes the length of x. Then it is well known that the smallest set [IN; SUB,LR] of functions from # # to # # containing IN and closed under substitution and limited recursion is exactly the collection PF of all functions computable in polynomial time on a deterministic Turing transducer [6, 17]. Note that in recent years several other machine independent characterizations of PF have been presented [2, 7, 9, 8] In what follows we will work with the above characterization. But it should be obvious that characterizations in which a di#erent set of initial functions or other closure ....
A. Cobham, The intrinsic computational di#culty of functions, in: Y. Bar-Hillel, ed., Logic, Methodology and Philosophy of Science II , North-Holland, Amsterdam, 1965, 24--30.
Naïve Type Theory - Constable (2002) (Correct)
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A. Cobham. The intrinsic computational di#culty of functions. In Y. BarHillel, editor, Proceedings of the
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