Communication complexity is the mathematical theory of such communication processes.
The simplest model that captures many of the issues in studying communication processes is the two-party model introduced by Yao. The communication complexity of this problem is the number of bits the players have to send to each other in order to determine the value of the function on an arbitrary input. This model and many of its variants have been widely studied. Communication complexity has many applications in different areas including computer networks, VLSI circuits and data structures. There are interesting connections between questions of communication complexity and computational complexity in other models.