Diagonalization and the complexity of programs

Starting from the definitions of predicative recursion and constructive diagonalization, we recall our specialized programming language that provides a resource-free characterization of register machines computing their output within polynomial time O(n^k), and exponential time O(n^n^k), for each finite k. We discuss the possibility of extending this characterization to a transfinite hierarchy of programs that captures the Grzegorczyk hierarchy of functions at elementary level. This is done by means of predicative operators, contrasting to previous results. We discuss the feasibility and the complexity of our diagonalization operator.