Control structures in programs and computational complexity

This thesis is concerned with analysing the impact of nesting (restricted) control structures in programs, such as primitive recursion or loop statements, on the running time or computational complexity. The method obtained gives insight as to why some nesting of control structures may cause a blow up in computational complexity, while others do not. The method is demonstrated for three types of programming languages..

Characterising Polytime through higher type Recursion

Rapport interne.It is shown how to restrict recursion on notation in all finite types so as to characterise the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types $!\sigma$, and by adding linear concepts to the lambda calculus

Implicit characterizations of FPTIME and NC revisited

Various simplified or improved and partly corrected well-known implicit characterizations of the complexity classes FPTIME and \NC are presented. Primarily, the interest is in simplifying the required simulations of various recursion schemes in the corresponding (implicit) framework and in developing those simulations in a more uniform way, based on a step-by-step comparison technique, thus consolidating groundwork in implicit computational complexity

Certifying

polynomial time and linear/polynomial space for imperative program

Ranking primitive recursions: The low grzegorczyk classes revisited

Abstract. Traditional results in subrecursion theory are integrated with the recent work in “predicative recursion ” by defining a simple ranking ρ of all primitive recursive functions. The hierarchy defined by this ranking coincides with the Grzegorczyk hierarchy at and above the linearspace level. Thus, the result is like an extension of the Schwichtenberg/Müller theorems. When primitive recursion is replaced by recursion on notation, the same series of classes is obtained except with the polynomial time computable functions at the first level