On the Complexity of Program Debugging Using Constraints for Modeling the Program’s Syntax and Semantics

Abstract

The use of model-based diagnosis for automated program debugging has been reported in several publications. The quality of the obtained results in terms of debugging accuracy is good. Unfortunately, most of the proposed models and techniques have very high computational needs. In this paper we focus on giving an explanation for the high computational needs of debugging. In particular, we propose a constraint representation of programs whose behavior is equivalent to the original programs. We further analyze the constraint representation to obtain its hypertree width, which is an indicator for the complexity of the corresponding constraint satisfaction problem. As constraint-based debugging is equivalent to constraint solving, the hypertree width is also an indicator for the debugging complexity. We further show that it is possible to construct arbitrarily complex programs such that their hypertree width is not bounded as indicated in previous literature.