A Refinement of the μ-measure for Stack Programs

We analyze the complexity of a programming language operating on stacks, introducing a syntactical measure σ such that to each program P a natural number σ(P) is assigned; the measure considers the influence on the complexity of programs of nesting loops and, simultaneously, of sequences of non-size-increasing subprograms. We prove that functions computed by stack programs of σ measure n have a length bound b∈En+2 (the n+2-th Grzegorczyk class), that is |f(w→)|≤b(|w→|). This result represents an improvement with respect to the bound obtained via the μ-measure presented in [L. Kristiansen and K.-H. Niggl, On the computational complexity of imperative programming languages. Theoretical Computer Science, to appear]