  The question of how much communication is required between collaborating
parties to compute a function of their data is of fundamental importance in the
fields of theoretical computer science and information theory. In this work,
the focus is on coming up with lower bounds on this. The information cost of a
protocol is the amount of information the protocol reveals to Alice and Bob
about each others inputs, and the information complexity of a function is the
infimum of information costs over all valid protocols. For the amortized case,
it is known that the optimal rate for the computation is equal to the
information complexity. Exactly computing this information complexity is not
straight forward however. In this work we lower bound information complexity
for independent inputs in terms of the Wyner common information of a certain
pair of random variables. We show a structural property for the optimal
auxiliary random variable of Wyner common information and exploit this to
exactly compute the Wyner common information in certain cases. The lower bound
obtained through this technique is shown to be tight for a non-trivial example
- equality (EQ) for the ternary alphabet. We also give an example to show that
the lower bound may, in general, not be tight.
