  Binary functions are a generalisation of the cocircuit spaces of binary
matroids to arbitrary functions. Every rank function is assigned a binary
function, and the deletion and contraction operations of binary functions
generalise matroid deletion and contraction. We give the excluded minor
characterisations for the classes of binary functions with well defined minors,
and those with an associated rank function. Within these classes, we also
characterise the classes of binary functions corresponding to polymatroids,
matroids and binary matroids by their excluded minors. This gives a new proof
of Tutte's excluded minor characterisation of binary matroids in the more
generalised space of binary functions.
