On the asymptotic behaviour of primitive recursive algorithms

Abstract

This paper develops a new semantics (the trace of a computation) that is used to study intensional properties of primitive recursive algorithms. It gives a new proof of the “ultimate obstination theorem” of L. Colson and extends it to the case when mutual recursion is permitted. The ultimate obstination theorem fails when other data types (e.g. lists) are used. I define another property ( the backtracking property) of the same nature but which is weaker than the ultimate obstination. This property is proved for every primitive recursive algorithm using any kind of data types.