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Journal of the ACM (JACM)
On the Structure of Polynomial Time Reducibility
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On the time and tape complexity of languages I
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Type two computational complexity
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The complexity of theorem-proving procedures
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On classes of computable functions
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On the Problem of Finding Natural Computational Complexity Measures
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Formal languages and their relation to automata
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On the density of honest subrecursive classes
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Augmented loop languages and classes of computable functions
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Implicit Computational Complexity for Higher Type Functionals
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Feasible Iteration of Feasible Learning Functionals
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Andrzej Grzegorczyk's Contribution to Computer Science
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The reducibility ''polynomial time computable in'' for arbitrary functions isintroduced. It generalizes Cook's definition from sets to arbitrary functions. A complexity-theoretic as well as a syntactic characterization is given and their equivalence is shown. This equivalence and the naturalness of both definitions give evidence that our notion is ''correct.'' The computable functions are classified into polynomial classes according to this reducibility. The ordering of these classes under set inclusion is studied. Honest classes are introduced and using them, the classification is related to the computational complexity of the functions classified. The algebraic structure of honest classes is also investigated. In Section II abstract subrecursive reducibilities are introduced. An axiomaticdefinition in purely recursion-theoretic terms is given; in particular, no reference to a particular machine model is needed. The definition is in the spirit of Strong's and Wagner's characterizations of basic recursive function theories. All known reducibilities are abstract reducibilities. The algebraic structure of abstract classes is explored.