Abstmct. 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 no 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 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 Btichi 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 Biichi automaton by means of a set of MFGs.

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We address the problem, proposed by Gerth, of verifying that a simplified version of the lazy caching algorithm of Afek, Brown, and Merritt is sequentially consistent. We specify the algorithm and sequential consistency in TLA + , a formal specification language based on TLA (the Temporal Logic of Actions). We then describe how to construct and check a formal TLA correctness proof.

We discuss a translation of Message Sequence Charts (MSCs) into the language PROMELA (we call this translation an`implementation') that is consistent with the formal semantics we have previously de ned for Message Flow Graphs and Message Sequence Charts, which handled the syntactic features with mathematical import from ITU-T recommendation Z.120. We report on experiments executing the PROMELA code using the XSPIN simulator and validator. In previous work we found that potential process divergence and non-local choice situations impose problems on implementations of MSCs, and we discuss how these impact our PROMELA translation and suggest solutions. Finally, we show how to model-check liveness requirements imposed on MSC speci cations. We use the PROMELA models obtained from our implementation, describe how to use control state propositions based on these models, use Linear Time Temporal Logic formulas to specify the liveness properties, and demonstrate the use of XSPIN as a model checker for these properties.