Formalization of graph search algorithms and its applications

This paper describes a formalization of a class of fixed-point problems on graphs and its applications. This class captures several well-known graph theoretical problems such as those of shortest path type and for data flow analysis. An abstract solution algorithm of the fixed-point 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 verification of model checking algorithms.