"True concurrency" has traditionally been distinguished from interleaving semantics in terms of partial vs. linear ordering of events. A distinction proposed by the speaker at POPL'91 instead represents concurrency by interpreting n concurrent atomic events as an n-dimensional cubical cell, leading to a notion of higher dimensional automaton. Although most of the subsequent development of this approach has taken homological algebra as its framework, there is a conceptually simpler formalization: extend the two-state Nielsen-Plotkin-Winskel event structure model with a third state, transition, to arrive at an extensional notion of concurrency. Independently but analogously, a fourth state, cancellation, permits an extensional notion of branching time. The definitions of the extant process algebra operations require little or no modification (depending on the operation) to accommodate these additional states, which have the additional benefit of permitting straightforward definitions for such notions as running time and termination which are problematic for two-state event structures.

This talk is based on a paper under the above title that has just appeared in MSCS 13:4.