Conference Paper

Calculating Polynomial Runtime Properties.

DOI: 10.1007/11575467_16 Conference: Programming Languages and Systems, Third Asian Symposium, APLAS 2005, Tsukuba, Japan, November 2-5, 2005, Proceedings
Source: DBLP

ABSTRACT Ane size-change analysis has been used for termination analysis of eager functional programming languages. The same style of analysis is also capable of compactly recording and calculating other properties of programs, including their runtime, maximum stack depth, and (relative) path time costs. In this paper we show how precise poly- nomial bounds on such costs may be calculated on programs, by a char- acterization as a problem in quantifier elimination. The technique is de- cidable, and complete for a class of size-change terminating programs with limited-degree polynomial costs. An extension to the technique al- lows the calculation of some classes of exponential-cost programs. We demonstrate the new technique by recording the calculation in numbers- of-function (or procedure) calls for a simple definition language, but it can also be applied to functional and imperative languages. The tech- nique is automated within the reduce computer algebra system.

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