A mathematical model for communicating sequential processes is given, and a number of its interesting and useful properties are stated and proved. The possibilities of nondetermimsm are fully taken into account.

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Abstract. FDR3 is a complete rewrite of the CSP refinement checker FDR2, incorporating a significant number of enhancements. In this paper we describe the operation of FDR3 at a high level and then give a detailed description of several of its more important innovations. This includes the new multi-core refinement-checking algorithm that is able to achieve a near linear speed up as the number of cores increase. Further, we describe the new algorithm that FDR3 uses to construct its internal representation of CSP processes-this algorithm is more efficient than FDR2's, and is able to compile a large class of CSP processes to more efficient internal representations. We also present experimental results that compare FDR3 to related tools, which show it is unique (as far as we know) in being able to scale beyond the bounds of main memory.

A space X is discretely absolutely star-Lindelöf if for every open cover U of X and every dense subset D of X, there exists a countable subset F of D such that F is discrete closed in X and St(F, U) = X, where St(F, U) = {U ∈ U : U ∩F = ∅}. We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed G δ-subspace.

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Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearly-ordered infinite domains and in which whole-place operations such as resets and transfers are possible. Data nets subsume several known classes of infinite-state systems, including multiset rewriting systems and polymorphic systems with arrays.We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which whole-place operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without whole-place operations, we establish that coverability, termination and boundedness for the latter class have non-primitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without whole-place operations has non-elementary complexity.

A complete set of algebraic laws is given for Dijkstra's nondeterministic sequential programming language. Iteration and recursion are explained in terms of Scott's domain theory as fixed points of continuous functionals. A calculus analogous to weakest preconditions is suggested as an aid to deriving programs from their specifications.

The parallel language CSP [H,1985], an earlier version of which was described in [H,1978], has become a major tool for the analysis of structuring methods and proof systems involving paxallellsm. The significance of CSP is in the elegance by which a few simply stated constructs (e.g., sequential and parallel composition, nondeterminlstic choice, concealment, and recursion) lead to a language capable of expressing the full complexity of distributed computing. The difficulty in achieving satisfactory semantic models containing these constructs has been in providing an adequate treatment of nondeterminism, deadlock, and divergence. Fortunately, as a result of an evolutionary development in [