Enhanced event structures: Towards a true concurrency semantics for E-LOTOS

Abstract

E-LOTOS is a standard process-algebraic language for formal specification of real-time concurrent and reactive systems. Its originally defined semantics is based on interleaving of events. In the present paper, we propose an enhanced kind of event structures and show how to employ them to give E-LOTOS processes a branching-time true concurrency semantics. The proposed event structures can model real-time processes with data handling and excel in concise representation of event renaming and synchronization.

Introduction

E-LOTOS [4], [19], an enhanced successor of LOTOS [3], [1], is one of the standard languages for formal specification of real-time concurrent and reactive systems. According to the operational semantics given in [4], an E-LOTOS specification characterizes a process by its readiness to engage into various kinds of atomic instantaneous events, where all internal process events are by definition anonymous and all concurrent events are represented as interleaved. That reflects the fact that LOTOS was originally intended for specification of “temporal ordering of observational behaviour” [3], where the possibility of simultaneous events was neglected.

Such characterization of a process often fails to provide sufficient information for its further refinement. For example, when refining an event into a process, one must know the relations of causality and conflict in which the event is engaged, because at least some of the events constituting its refinement are supposed to inherit them [6]. One might also want to identify events which are truly concurrent, so that their execution may be delegated to different concurrent components of a system. Hence, it is convenient to model a process by its events and their relationships, i.e., by its event structure.

With their detailed representation of process behaviour, event-structure models are ideal not only for refinement of events, but also for refinement of their relationships, necessary, for example, when designing a distributed implementation of a process, i.e., refining the relationships into a coordination protocol [16]. On the other hand, event structures refrain from modelling process architecture, following the idea that grouping of events into subprocesses is, like their assignment to gates, just a matter of interpretation [12]. Hence, an event structure is indeed just a collection of events and relationships, i.e., a set of orthogonal process properties.

The syntactic and semantic simplicity makes event structures easy to use and ideal for incremental design. Elements of an event structure may be added and removed at will, although it is advisable to take care that the structure stays within a class which can be easily manipulated with the available tools (e.g., to avoid causal ambiguity [20]). As increasingly more powerful manipulation tools are available, we in this paper limit our attention to the expressiveness of event structures.

A process-algebraic specification describes a set of elementary processes and their hierarchical composition. Elementary processes often correspond to individual events and composition operators provide information on their relationships. The problem is that when the operands of a composition operator are themselves compound processes, the relationships between their constituent events are described only implicitly. To overcome the problem, process-algebraic languages are being furnished with event-structure semantics.

For LOTOS without data, an event-structure semantics was proposed in [13]. The semantics was extended to timed processes [11], and subsequently employed [2] (still without data) for ET-LOTOS [14], a predecessor of E-LOTOS. In the present paper, we propose an event-structure semantics for E-LOTOS.

The proposed true concurrency semantics for E-LOTOS is not the only contribution of the paper. Perhaps even more important is the newly developed kind of event structures, which we name enhanced event structures, because in the name E-LOTOS, “E” stands for “enhanced.” Enhanced event structures can model real-time processes with data handling and excel in concise representation of event renaming and synchronization.

The paper is organized as follows: In Section 2, we analyse the intuitive semantics of E-LOTOS processes and gradually develop a kind of event structures sufficiently expressive for their elegant modelling. Section 3 contains a detailed study of event-structure semantics of elementary E-LOTOS processes and of individual process composition operators. Section 4 comprises a discussion and conclusions.