Timed Event Structures Research Articles

Logic Unification of Behavioral Equivalences of Timed Event Structures

We propose a uniform logic characterization of some timed extensions of partial order based equivalences (pomset trace equivalence, testing equivalence, history preserving bisimulation, and hereditary history preserving bisimulation) in the setting of a true concurrency model timed event structures.

Formal semantics for interactive music scores: a framework to design, specify properties and execute interactive scenarios

Most interactive scenarios are based on informal specifications, so that it is not possible to formally verify properties of such systems. We advocate the need for a general and formal model aiming at ensuring safe executions of interactive multimedia scenarios. Interactive scores (is) is a formalism based on temporal constraints to describe interactive scenarios. We propose new semantics for is based on timed event structures (TES). With such a semantics, we can specify more properties of the system, in particular, properties about execution traces, which are difficult to specify as constraints. We also present an operational semantics of is based on the non-deterministic timed concurrent constraint calculus and we relate such a semantics to the TES semantics. With the operational semantics, we can describe the behaviour of scores whose timed object durations can be arbitrary integer intervals.

Composition methods for constructing characteristic formulas for dense-time models

In verification of complex computing systems, the concept of testing equivalence is frequently used. One of the ways to solve the problem of recognizing timed testing equivalences in the framework of the model of timed event structures with internal actions is to reduce it to formula verification on a model (model-checking). To this end, logical formulas characterizing timed event structure up to test pre-orders are constructed. In the paper, composition methods for characteristic formulas that do not rely on region and class graphs are considered, which simplifies construction of the characteristic formulas.

Semantic domains of timed event structures

In the paper, timed extensions of various classes of event structures and marked Scott domains are studied, categories of these models are constructed, and their properties are examined. In addition, based on category-theoretic methods, relationship between the timed structures and marked Scott domains is established.

Event-based operational semantics and a consistency result for real-time concurrent processes with action refinement

In this paper an event-based operational interleaving semantics is proposed for real-time processes, for which action refinement and a denotational true concurrency semantics are developed and defined in terms of timed event structures. The authors characterize the timed event traces that are generated by the operational semantics in a denotational way, and show that this operational semantics is consistent with the denotational semantics in the sense that they generate the same set of timed event traces, thereby eliminating the gap between the true concurrency and interleaving semantics.

Metric semantics for true concurrent real time

This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langerak's bundle event structures, a variant of Winskel's event structures. The distance function of the metric is based on the amount of time to which event structures do ‘agree’. We show that this intuitive notion of distance is a pseudo-metric (but not a metric) on the set of timed event structures. A generalisation to equivalence classes of timed event structures in which we abstract from event identities and non-executable events (events that can never occur) is shown to be a complete ultra-metric space. We present an operational semantics for the considered language and show that the metric semantics is an abstraction of it. The operational semantics is characterised by the absence of synchronisation on the advance of time as opposed to the operational semantics of most real-time calculi. The consistency between our metric and an existing cpo-based denotational semantics is briefly investigated.

Analysis of equivalence relations of event structures with continuous time

Notions of testing and bisimulation equivalencies for concurrent nondeterministic processes in real (continuous) time are introduced and analyzed. Processes are represented by timed event structures. Conditions under which the equivalencies defined coincide are established, and algorithms for deciding equivalence are presented.

Model checking on timed-event structures

We propose a new style of model checking of timed transition systems, where instead of reasoning about the timing of states with specific properties, we reason about the timings of events with specific properties. This shift in paradigm appears to be useful for verification of edge triggered control paths, where we are more interested in the timings of changes in signal values. We propose a temporal logic, event-triggered timed computation tree logic (ETCTL), which allows the specification of event properties such as posedge(signal) and negedge(signal) along with real time computation tree logic (RTCTL) properties. We show that all ETCTL properties are interval independent, that is, their truth can never change on states between successive events. By virtue of the interval independent property, reasoning about timings of events (using ETCTL) is more efficient computationally than reasoning about general timed properties. We present a labeling algorithm, and suggest extensions to automata theoretic and symbolic approaches.