On the complexity of programs with nested loops

Given a programming language operating on stacks, we introduce a syntactical measure mu such that, a natural number mu(P) is assigned to each program P. The measure considers how the presence of loops defined over size-increasing (and/or non-size-increasing) subprograms influences the complexity of the program itself. We prove that a generic function f computed by a stack program with mu-measure n has length bound b in E^(n+2) (the n + 2-th Grzegorczyk class), that is |f( w)| <= b(| w|). Thus, we have a syntactical characterization of the functions belonging to the Grzegorczyk hierarchy; this result represents an improvement with respect to previous similar results.