Branching vs. Linear Time: Semantical Perspective

Abstract

The discussion in computer-science literature of relative merits of linear- versus branching-time frameworks goes back to early 1980s. One of beliefs dominating this discussion has been that linear-time framework is not expressive enough semantically, making linear-time logics lacking in expressiveness. In this work we examine branching-linear issue from perspective of process equivalence, which is one of most fundamental notions in concurrency theory, as defining a notion of process equivalence essentially amounts to defining semantics for processes. Over last three decades numerous notions of process equivalence have been proposed. Researchers in this area do not anymore try to identify right notion of equivalence. Rather, focus has shifted to providing taxonomic frameworks, such as the linear-branching spectrum, for many proposed notions and trying to determine suitability for different applications. We revisit here this issue from a fresh perspective. We postulate three principles that we view as fundamental to any discussion of process equivalence. First, we borrow from research in denotational semantics and take observational equivalence as primary notion of equivalence. This eliminates many testing scenarios as either too strong or too weea. Second, we require description of a process to fully specify all relevant behavioral aspects of process. Finally, we require observable process behavior to be reflected in its input/output behavior. Under these postulates distinctions between linear and branching semantics tend to evaporate. As an example, we apply these principles to framework of transducers, a classical notion of state-based processes that dates back to 1950s and is well suited to hardware modeling. We show that our postulates result in a unique notion of process equivalence, which is trace based, rather than tree based.