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Let F be any effective mapping from total functions on the integers to total functions. Composition and iterated composition are examples of such mappings. The "operator speed-up" theorem in this paper establishes the existence of a computable function f such that for any program computing f(x) in p1(x) steps for all x, there is another program computing f(x) in p2(x) steps and F(p2) ≪ P1...
The purpose of this paper is to generalize the methods of automata theory to accommodate infinite input alphabets and to propose a method of describing computer languages such as ALGOL-60 with more reliance on grammatical methods and less reliance on semantic constraints. Our chief concern is a natural generalization of a context-free grammar which we call a context-free property grammar. The generalization...
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