Concurrent processes and the interchange entropy

Concurrency is the study of systems involving multiple processes. The order of events in a concurrent system is unpredictable because of the independence of events occurring in the individual processes [1]. Trace theory [2] is a model for the execution of concurrent processes which employs congruence or interchange classes of words over partially commutative alphabets. These interchange classes generalize the more familiar notions of strings and type classes. We consider a rate distortion problem in which the objective is to reproduce a string which is equivalent to the original string. This leads to a new graph entropy called the interchange entropy, and we provide some of its basic properties.