Stanley S. Wainer

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In this paper we use methods of proof theory to assign ordinals to classes of (terminating) programs, the idea being that the ordinal assignment provides a uniform way of measuring computational complexity \in the large". We are not concerned with placing prior (e.g. polynomial) bounds on computation{length, but rather with general methods of assessing the(More)
There is a quite natural way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable (slow growing rather than fast growing).(More)
The class of all recursive functions fails to possess a natural hierarchical structure, generated predicatively from “within”. On the other hand, many (proof-theoretically significant) sub-recursive classes do. This paper attempts to measure the limit of predicative generation in this context, by classifying and characterizing those (predictably(More)