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Two restricted imperative programming languages are considered: One is a slight modification of a loop language studied intensively in the literature, the other is a stack programming language over an arbitrary but fixed alphabet, supporting a suitable loop concept over stacks. The paper presents a purely syntactical method for analysing the impact of… (More)

We present a new method for inferring complexity properties for imperative programs with bounded loops. The properties handled are: polynomial (or linear) boundedness of computed values, as a function of the input; and similarly for the running time. It is well known that complexity properties are undecidable for a Turing-complete programming language. Much… (More)

We present a method for certifying that the values computed by an imperative program will be bounded by polynomials in the program's inputs. To this end, we introduce mwp-matrices and define a semantic relation |= C : M where C is a program and M is an mwp-matrix. It follows straightforwardly from our definitions that there exists M such that |= C : M holds… (More)

We introduce two hierarchies of unknown ordinal height. The hierarchies are induced by natural fragments of a calculus based on finite types and Gödel's T , and all the classes in the hierarchies are uniformly defined without referring to explicit bounds. Deterministic complexity classes like logspace, p, pspace, linspace and exp are captured by the… (More)