The main purpose of this paper is to exhibit non-algebraic problems that are computationally equivalent to computing the integer determinant. For this purpose, some graph-theoretic counting problems are shown to be equivalent to the integer determinant problem under suitable reducibilities. Those are the problems of counting the number of all paths between two nodes of a given acyclic digraph, the number of all smallest length paths between two nodes of a given undirected graph, the number of… CONTINUE READING