In this work, we consider gas sensor arrays comprised of fewer MOFs than degrees of freedom in the gas composition (M < G). The mapping a : x → m under a sensor array with M < G is generally non-injective (manyto-one). Consequently, the inverse problem of determining the gas composition x from the sensor response m is underdetermined; typically, many gas compositions can produce the observed response. In the inverse problem, observation of each MOF's response, generally, provides one independent constraint, m i = a i (x), on the gas composition. For M < G, the response of the sensor array places an insufficient number of constraints on the gas composition to uniquely determine it.