Vector controlled concurrent systems. I: Basic classes.

*(English)*Zbl 0713.68024This Part I of the authors’ research on a formal model of concurrent systems, called Vector Controlled Concurrent Systems (VCCS) and generalizing the path expressions mechanism of COSY, contains mostly a motivation behind the model and main definitions. A VCCS S consists of a fixed number (say, n) of sequential (nondeterministic) components and a global synchronization mechanism (controller). Any \(i\)-th component of S is represented by a formal language \({\mathcal L}_ i\) with letters representing actions. The controller of S is represented by a language C over an alphabet \(\Delta\) consisting of n-dimensional vectors whose entries are letters or the empty word. Under vertical representation of vector letters in \(w\in C\) let \(w(i)\) denote the word written at the \(i\)- th row of \(w\) (with the empty word components cancelled). Then the behavior of S is described as the set \(V(S)=\{<w(1),...,w(n)>\), where \(w\in C\) and \(w(i)\in {\mathcal L}_{i}\}\) (this definition of V(S) is obtained by an easy reformulation of one of equivalent definitions contained in the paper). Three subclasses of VCCS’s are distinguished. In the first one \(C=\Delta^*\) (it is interpreted as static synchronization). In two other cases synchronization vectors may depend on history and are defined by coloured Petri nets or depend on states of individual sequential components. The definition of VCCS is very close to (and generalizes in some directions) the definition of synchronized systems of processes introduced by M. Nivat and A. Arnold. In the concluding section some differences between these models, mostly of the methodological nature, are indicated.

Reviewer: M.Val’ev