Parametric Strategy Iteration

15 pages•Published: December 4, 2014

Abstract

Program behavior may depend on parameters, which are either configured
before compilation time, or provided at runtime, e.g., by sensors or other input devices.
Parametric program analysis explores how different parameter settings may affect the
program behavior.

In order to infer invariants depending on parameters, we introduce parametric strategy iteration.
This algorithm determines the precise least solution of systems of integer equations depending
on surplus parameters. Conceptually, our algorithm performs ordinary strategy iteration
on the given integer system for all possible parameter settings in parallel.
This is made possible by means of region trees to represent the occurring piecewise affine functions.
We indicate that each required operation on these trees is polynomial-time if only constantly many
parameters are involved.

Parametric strategy iteration for systems of integer equations
allows to construct parametric integer interval analysis
as well as parametric analysis of differences of integer variables.
It thus provides a general technique to realize precise parametric
program analysis if numerical properties of integer variables are of concern.

Keyphrases: abstract interpretation, parametric program analysis, strategy iteration

In: Temur Kutsia and Andrei Voronkov (editors). SCSS 2014. 6th International Symposium on Symbolic Computation in Software Science, vol 30, pages 62-76.

Links:	https://easychair.org/publications/paper/Nzl
	https://doi.org/10.29007/c4kg