The transitive closures of matrices over distributive lattices

Abstract

In this paper, we study the transitive closure for any matrix over an arbitrary distributive lattice. It is shown that any matrix over a distributive lattice has a transitive closure. This existential result can be turned into an explicit expression. It is well-known that the Warshall’s algorithm is a more efficient algorithm for computing transitive closure of a relation on a finite universe. In order to give a more efficient algorithm for the transitive closure of a lattice matrix, the Warshall’s algorithm, which is used for computing transitive closure of a matrix over an arbitrary distributive lattice, is established.