Automatic inference of upper bounds for recurrence relations in cost analysis. (English) Zbl 1149.68345

Albert, Elvira; Arenas, Puri; Genaim, Samir; Puebla, Germán

Alpuente, María (ed.) et al., Static analysis. 15th international symposium, SAS 2008, Valencia, Spain, July 16–18, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-69163-1/pbk). Lecture Notes in Computer Science 5079, 221-237 (2008).

Summary: The classical approach to automatic cost analysis consists of two phases. Given a program and some measure of cost, we first produce recurrence relations (RRs) which capture the cost of our program in terms of the size of its input data. Second, we convert such RRs into closed form (i.e., without recurrences). Whereas the first phase has received considerable attention, with a number of cost analyses available for a variety of programming languages, the second phase has received comparatively little attention. In this paper we first study the features of RRs generated by automatic cost analysis and discuss why existing computer algebra systems are not appropriate for automatically obtaining closed form solutions nor upper bounds of them. Then we present, to our knowledge, the first practical framework for the fully automatic generation of reasonably accurate upper bounds of RRs originating from cost analysis of a wide range of programs. It is based on the inference of ranking functions and loop invariants and on partial evaluation.
For the entire collection see [Zbl 1142.68002].

MSC:

68N30

Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)

Software:

PURRS