THE COVERABILITY PROBLEM IN INPUT-OUTPUT SYSTEMS

The notion of a vector replacement system, developed in the computer science literature, is used to analyze the reachability problem in integer-valued input-output models. An integer-valued input-output system with initial resources is a 5-tuple [n, m, A, B, mu], where n is the number of commodities, m the number of production processes, A is the n x m input matrix, B is the n x m output matrix and mu is-an-element-of R(n) is the initial vector of resources. The elements of A, B and mu are non-negative integers. A vector mu' is reachable from mu if it is possible to transform mu into mu' through a sequence of production processes, without ever violating the feasibility constraint represented by the available resources.