Quantifying communication in synchronized languages

A mutual information rate is proposed to quantitatively evaluate inter-process synchronized communication. For finite-state processes with implicit communication that can be described by a counting language, it is shown that the mutual information rate is effectively computable. When the synchronization always happens between the same two symbols at the same time (or with a fixed delay), the mutual information rate is computable. In contrast, when the delay is not fixed, the rate is not computable. Finally, it is shown that some cases exist where the mutual information rate is not computable.