On tiered small jump operators

Predicative analysis of recursion schema is a method to characterizecomplexity classes like the class FPTIME of polynomial time computablefunctions. This analysis comes from the works of Bellantoni and Cook, andLeivant by data tiering. Here, we refine predicative analysis by using aramified Ackermann's construction of a non-primitive recursive function. Weobtain a hierarchy of functions which characterizes exactly functions, whichare computed in O(n^k) time over register machine model of computation. Forthis, we introduce a strict ramification principle. Then, we show how todiagonalize in order to obtain an exponential function and to jump outsidedeterministic polynomial time. Lastly, we suggest a dependent typedlambda-calculus to represent this construction