Underapproximation of Procedure Summaries for Integer Programs

TL;DR

This paper introduces a method to underapproximate procedure summaries of recursive integer programs using existing non-recursive analyzers, capturing unbounded behaviors and identifying classes where exact summaries are achievable.

Contribution

It extends non-recursive analysis techniques to recursive programs, enabling underapproximation and exact summary computation for certain classes.

Findings

Method successfully underapproximates recursive procedures.

Identifies classes of recursive programs with exact summaries.

Experimental results demonstrate practical effectiveness.

Abstract

We show how to underapproximate the procedure summaries of recursive programs over the integers using off-the-shelf analyzers for non-recursive programs. The novelty of our approach is that the non-recursive program we compute may capture unboundedly many behaviors of the original recursive program for which stack usage cannot be bounded. Moreover, we identify a class of recursive programs on which our method terminates and returns the precise summary relations without underapproximation. Doing so, we generalize a similar result for non-recursive programs to the recursive case. Finally, we present experimental results of an implementation of our method applied on a number of examples.