A mathematical framework for automated bug localization

TL;DR

This paper introduces a mathematical framework that models program execution as a graph and uses cut-sets to automate bug localization through graph pruning techniques.

Contribution

It presents a novel graph-based mathematical model for bug localization and a pruning algorithm to identify faulty program segments automatically.

Findings

Framework effectively models program execution as a graph.

Pruning algorithm successfully localizes bugs.

Provides a formal basis for automated debugging tools.

Abstract

In this paper, we propose a mathematical framework for automated bug localization. This framework can be briefly summarized as follows. A program execution can be represented as a rooted acyclic directed graph. We define an execution snapshot by a cut-set on the graph. A program state can be regarded as a conjunction of labels on edges in a cut-set. Then we argue that a debugging task is a pruning process of the execution graph by using cut-sets. A pruning algorithm, i.e., a debugging task, is also presented.