Formalization of Graph Search Algorithms and Its Applications

This paper describes a formalization of a class of xed-point problems on graphs and its applications. This class captures several wellknown graph theoretical problems such as those of shortest path type and for data ow analysis. An abstract solution algorithm of the xedpoint problem is formalized and its correctness is proved using a theorem proving system. Moreover, the validity of the A* algorithm, considered as a specialized version of the abstract algorithm, is proved by extending the proof of the latter. The insights we obtained through these formalizations are described. We also discuss the extension of this approach to the veri cation of model checking algorithms.