Parametric Strategy Iteration

Program behavior may depend on parameters, which are either configuredbefore compilation time, or provided at runtime, e.g., by sensors or other input devices.Parametric program analysis explores how different parameter settings may affect theprogram 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 dependingon surplus parameters. Conceptually, our algorithm performs ordinary strategy iterationon 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 manyparameters are involved.Parametric strategy iteration for systems of integer equationsallows to construct parametric integer interval analysisas well as parametric analysis of differences of integer variables.It thus provides a general technique to realize precise parametricprogram analysis if numerical properties of integer variables are of concern.