# Process algebra reconsidered

Paper is here.

The following incorrect claim is not unusual in the process algebra literature.

Basically, what is missing [in classical automata theory] is the notion of interaction: during the execution from initial state to final state, a system may interact with another system. This is needed in order to describe parallel or distributed systems, or so-called reactive systems. When dealing with interacting systems, we say we are doing concurrency theory, so concurrency theory is the theory of interacting, parallel and/or distributed systems.[Bae05]

Actually a sophisticated notion of state machine product was developed for representing composition of “interacting” state machines starting in the 1950s[HS66]. A general survey can be found in a monograph by Gecseg[Gec86], Domosi provides a more modern, more algebraic treatment [DN04] and [Yod09] provides practical techniques for construction of complex products.

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The reader familiar with the process algebra literature will note that such an effort must find a way to model the non-determinism that is so fundamental to the process algebra world-view. Since deterministic programs are used to produce pseudo-random number sequences and to model Brownian motion and even the stock market (perhaps not the best example at this date) the problem is easier to solve than it appears at first. Section 4 will include a short discussion on the difference between “real” non-determinism and simulated non-determinism, but certainly there is nothing in the basic axiom set of Milner’s original process algebra that notices this distinction as far as I can see.