Linear vs. branching time: A semantical perspective

The discussion of the relative merits of linear versus branching-time goes back to early 1980s. The dominating belief has been that the linear-time framework is not expressive enough semantically, marking linear-time logics as weak. Here we examine this issue from the perspective of process equivalence, one of the most fundamental notions in concurrency theory. We postulate three principles that we view as fundamental to any discussion of process equivalence. First, we take contextual equivalence as the primary notion of equivalence. Second, we require the description of a process to fully specify all relevant behavioral aspects of the process. Finally, we require observable process behavior to be reflected in input/output behavior. Under these postulates the distinctions between the linear and branching semantics tend to evaporate. Applying them to the framework of transducers, we show that our postulates result in a unique notion of process equivalence, which is trace based, rather than tree based

Traces, pomsets, fairness and full abstraction for communicating processes

Abstract. We provide a denotational trace semantics for processes with synchronous communication and a form of weakly fair parallelism. The semantics is fully abstract: processes have the same trace sets if and only if their communication behaviors are identical in all contexts. The model can easily be adapted for asynchronously communicating processes, or for shared-memory parallel programs. We also provide a partial-order semantics, using pomsets adapted for synchronization and our form of fairness. The pomset semantics can also be adjusted to model alternative paradigms. The traces of a process can be recovered from the pomset semantics by taking all fair interleavings consistent with the partial order.

A semantics for concurrent separation logic

AbstractWe present a trace semantics for a language of parallel programs which share access to mutable data. We introduce a resource-sensitive logic for partial correctness, based on a recent proposal of O’Hearn, adapting separation logic to the concurrent setting. The logic allows proofs of parallel programs in which “ownership” of critical data, such as the right to access, update or deallocate a pointer, is transferred dynamically between concurrent processes. We prove soundness of the logic, using a novel “local” interpretation of traces which allows accurate reasoning about ownership. We show that every provable program is race-free