The paper introduces a model for processing systems which provides 'environment' to the abstract notion of process as introduced by Nivat . A basic component of the model is a protection mechanism which is general enough to capture as particular instances known protection strategies (e.g., take, grant, create, parameter passing) [5, 8, 9]. Decision problems associated with these systems are discussed for both cases: processes with infinite and finite behaviours. Solvability results are obtained for the safety problem: as a corollary we get the solvability result of Beauquier in the context of his processes . Unsolvability results are also derived. A concept of compatibility is introduced for processes acting in parallel subject to some synchronization condition. We show that the traversing from rational to algebraic systems can take the compatibility problem from solvable to unsolvable. © 1983.
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