Abstract We give a semantics for Message Flow Graphs (MFGs), which play the role for interprocess communication that Program Dependence Graphs play for control flow in parallel processes. MFGs have been used to analyse parallel code, and are closely related to Message Sequence Charts and Time Sequence Diagrams in telecommunications systems. Our requirements are firstly, to determine unambiguously exactly what execution traces are specified by an MFG, and secondly, to use a finite-state interpretation. Our methods function for both asynchronous and synchronous communications. From a set of MFGs, we define a transition system of global states, and from that a Büchi automaton by considering safety and liveness properties of the system. In order easily to describe liveness properties, we interpret the traces of the transition system as a model of Manna-Pnueli temporal logic. Finally, we describe the expressive power of MFGs by mimicking an arbitrary Büchi automaton by means of a set of MFGs.

The concepts of binary constraint satisfaction problems can be naturally generalized to the relation algebras of Tarski. The concept of path-consistency plays a central role. Algorithms for path-consistency can be implemented on matrices of relations and on matrices of elements from a relation algebra. We give an example of a 4-by-4 matrix of infinite relations on which on iterative local path-consistency algorithm terminates. We give a class of examples over a fixed finite algebra on which all iterative local algorithms, whether parallel or sequential, must take quadratic time. Specific relation algebras arising from interval constraint problems are also studied: the Interval Algebra, the Point Algebra, and the Containment Algebra.

We present an algorithm for analyzing deadlock and for constructing sequentializations of a class of communicating sequential processes. The algorithm may be used for deadlock detection in parallel and distributed programs at compile time, or for debugging purposes at run time. The algorithm generates a data structure we call the flow graph, which contains all you need to know about the communications between the processes. If the algorithm is used only for debugging, it is not necessary to retain a copy of the flow graph. Both static deadlock analysis and trace generation are linear in the size of the (minimum) flow graph we construct.