  The problem of distributed function computation is studied, where functions
to be computed is not necessarily symbol-wise. A new method to derive a
converse bound for distributed computing is proposed; from the structure of
functions to be computed, information that is inevitably conveyed to the
decoder is identified, and the bound is derived in terms of the optimal rate
needed to send that information. The class of informative functions is
introduced, and, for the class of smooth sources, the optimal rate for
computing those functions is characterized. Furthermore, for i.i.d. sources
with joint distribution that may not be full support, functions that are
composition of symbol-wise function and the type of a sequence are considered,
and the optimal rate for computing those functions is characterized in terms of
the hypergraph entropy. As a byproduct, our method also provides a conceptually
simple proof of the known fact that computing a Boolean function may require as
large rate as reproducing the entire source.
