Min algebraic duality

Min algebra has been used (Cuninghame-Greem [2], Hoffman [3]) to obtain results in operations research and graph theory. It has previously been seen primarily as an efficient way to describe a system of minimum relations. In this note we develop an elimination scheme for inductively solving systems of min algebraic equations and then prove a theorem of the alternative which is closely related to one of the duality models described in [3]. This work was developed in relation to tag systems [1]. These results provide a first step toward broadening min algebra from a modeling scheme to a solution technique.