Abstract
Several classical approaches to higher type computability are described and compared. Their suitability for providing a basis for higher type complexity theory is discussed. A class of polynomial time functional is described and characterized. A new result is proved in Section 8, showing that an intuitively polynomial time functional is in fact not in the class described.
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Cook, S.A. (1992). Computability and Complexity of Higher Type Functions. In: Moschovakis, Y.N. (eds) Logic from Computer Science. Mathematical Sciences Research Institute Publications, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2822-6_3
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DOI: https://doi.org/10.1007/978-1-4612-2822-6_3
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