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A Concrete Approach to Abstract Recursive Definitions

Author(s)
Wand, Mitchell
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Abstract
We introduce a non-categorical alternative to Wagner's Abstract Recursive Definitions [Wg-1,2] using a generalization of the notion of clone called a u-clone. Our more concrete approach yields two new theorems: 1.) the free u-clone generated by a ranked set is isomorphic to the set of loop-representable flow diagrams with function symbols in the set, 2.) For every element of a u-clone there is an expression analogous to a regular expression. Several well-known theorems of language and automata theory are drawn as special cases of this theorem.
Date issued
1972-06-01
URI
http://hdl.handle.net/1721.1/6207
Other identifiers
AIM-262
Series/Report no.
AIM-262

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  • AI Memos (1959 - 2004)

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