Some Existence and Preservation Results for Optimal Fixpoints
نویسنده
چکیده
Optimal fixpoints of recursive operators extract maximum consistent information from recursive definitions. Although the optimal fixpoint always exists for a recursive operator, it can be uncomputable. The paper considers the restriction of the recursive operator to computable inputs and the set of consistent fixpoints induced by this restriction. The properties of the greatest element of this set is studied, particularly, its relation to computable optimal fixpoint. It has been shown in previous work that the greatest consistent fixpoint of a restricted operator may differ from the computable optimal fixpoint. The article illustrates that the greatest consistent fixpoint can also disappear as a result of the restriction.
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