Generalisation of Dedekind's problem of the enumeration of coherent structures

Synopsis In the context of reliability theory, two definitions are given for coherent functions of n variables, where both function and variables can take any of l possible levels. The enumeration problem for such functions is discussed and several recursive bounds are derived. In the case of l = 2 (the Dedekind problem ) a recursive upper bound is derived which is better than the previous best explicit upper bound for n < 15, and also provides a systematic improvement on this bound for larger values of n .