Formal treatment of a family of fixed-point problems on graphs by CafeOBJ

A family of well-known problems on graphs, including the shortest path problem and the data flow analysis problem, can be uniformly formulated as a fixed-point problem on graphs. We specify this problem and its solution algorithm in a highly abstract manner, fully exploiting the parametrized module construct of CafeOBJ, an algebraic specification language. The objective of our research is to explore the effectiveness of formal methods, applying them not just to specific safety-critical programs but to general problems covering a wide range of applications.