Abstract
This paper discusses refinements of the natural ordering of them-degrees (1-degrees) of strong recursive reducibility classes. Such refinements are obtained by posing complexity conditions on the reduction function. The discussion uses the axiomatic complexity theory and is hence very general. As the main result it is proved that if the complexity measure is required to be linearly bounded (and space-like), then a natural class of refinements forms a lattice with respect to a natural ordering upon them.
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Bibliography
Manuel Blum,A machine-independent theory of the complexity of the recursive functions,Journal of the ACM Vol 14, No. 2 (1967), pp. 322–336.
W. Brainerd &L. Landweber,Theory of Computation, John Wiley & Sons, New York 1974.
Manuel Lerman,The degrees of unsolvability: Some recent results, In:F. R. Drake &S. S. Wainer (eds):Recursion Theory: its Generalisations and Applications, Cambridge University Press, Cambridge 1980.
Michael Machtey &Paul Young,An Introduction to the General Theory of Algorithms, North-Holland, New York 1978.
Odifreddi Piergiorgio,Strong reducibilities,Bulletin of the American Mathematical Society 4 (1981), pp. 37–86.
Hartley Rogers Jr.,Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York (1967).
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Talja, J. On the complexity-relativized strong reducibilites. Stud Logica 42, 259–267 (1983). https://doi.org/10.1007/BF01063845
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DOI: https://doi.org/10.1007/BF01063845