Interprocedural Reachability for Flat Integer Programs

TL;DR

This paper investigates the decidability of reachability in programs with integer data and procedure calls, establishing that it is decidable in Nexptime for certain classes of relations and transformations.

Contribution

It introduces a method to analyze interprocedural reachability in flat integer programs with octagonal relations, providing tight bounds and complexity results.

Findings

Reachability is decidable in Nexptime for programs with octagonal relations.

Program transformation reduces interprocedural analysis to procedure-less programs.

Complexity bounds are tight, with Np-completeness under certain parameters.

Abstract

We study programs with integer data, procedure calls and arbitrary call graphs. We show that, whenever the guards and updates are given by octagonal relations, the reachability problem along control flow paths within some language w1* ... wd* over program statements is decidable in Nexptime. To achieve this upper bound, we combine a program transformation into the same class of programs but without procedures, with an Np-completeness result for the reachability problem of procedure-less programs. Besides the program, the expression w1* ... wd* is also mapped onto an expression of a similar form but this time over the transformed program statements. Several arguments involving context-free grammars and their generative process enable us to give tight bounds on the size of the resulting expression. The currently existing gap between Np-hard and Nexptime can be closed to Np-complete when a certain parameter of the analysis is assumed to be constant.