An Operator Embedding Theorem for Complexity Classes of Recursive Functions
Let F (t) be the set of functions computable by some machine using no more than t(x) machine steps on all but finitely many arguments x. If we order the - classes under set inclusion as t varies over the recursive functions, then it is natural to ask how rich a structure is obtained. We show that th...
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Published: |
2023
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Online Access: | https://hdl.handle.net/1721.1/148861 |
Summary: | Let F (t) be the set of functions computable by some machine using no more than t(x) machine steps on all but finitely many arguments x. If we order the - classes under set inclusion as t varies over the recursive functions, then it is natural to ask how rich a structure is obtained. We show that this structure is very rich indeed. If R is any countable partial order and F is any total effective operator, then we show that there is a recursively enumerable sequence of... |
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