Irina Virbitskaite

Timed Delay Bisimulation is an Equivalence Relation for Timed Transition Systems

Timed transition systems are a widely studied model for real-time systems. The intention of the paper is to show the applicability of the general categorical framework of openmaps in order to prove that timed delay equivalence is indeed an equivalence relation in the setting of timed transition systems with invariants. In particular, we define a category of the model under consideration and an accompanying (sub)category of observations to which the corresponding notion of open maps is developed. We then use the open maps framework to obtain an abstract equivalence relation which is established to coincide with timed delay bisimulation.

A Categorical View of Timed Behaviours

Timed transition systems are a widely studied model for real-time systems. The intention of the paper is to show how several categorical (open maps, path-bisimilarity and coalgebraic) approaches to an abstract characterization of bisimulation relate to each other and to the numerous suggested behavioural equivalences of linear time - branching time spectrum, in the setting of timed transition systems.

Observational Semantics for Timed Event Structures

The paper is contributed to develop a family of observational equivalences for timed true concurrent models. In particular, we introduce three different semantics (based on interleaving, steps, and partial orders of actions) for timed trace and timed bisimulation equivalences in the setting of event structures with dense time domain. We study the relationship between these three approaches and show their discriminating power. Furthermore, when dealing with particular subclasses of the model under consideration such as sequential and deterministic timed event structures there is no difference between a more concrete or a more abstract approach.

Configuration- and Residual-Based Transition Systems for Event Structures with Asymmetric Conflict

In order to associate a transition system with an event structure, it is customary to use configurations, constructing a transition system by repeatedly adding executable events. It is also possible to use residuals, constructing a transition system by repeatedly deleting non-executable events. The present paper proposes a systematic investigation of how the two methods are interrelated. The focus will be on asymmetric versions of prime, bundle, and dual event structures. For each of them, configuration-based and residual-based transition system semantics will be defined. The pairwise bisimilarity of the resulting transition systems will be proved, considering interleaving, multiset, and pomset semantics.

Comparing Semantics Under Strong Timing of Petri Nets

The intention of the note is towards a framework for developing, studying and comparing observational semantics in the setting of a real-time true concurrent model. In particular, we introduce trace and bisimulation equivalences based on interleaving, step and causal net semantics in the setting of Petri nets with strong timing, i.e. Petri nets whose transitions are labeled with time firing intervals, can fire only if their lower time bounds are attained, and are forced to fire when their upper time bounds are reached. We deal with the relationships between the equivalences showing the discriminating power of the approaches of the linear-time – branching-time and interleaving – partial order spectra. This allows studying in complete detail the timing behaviour in addition to the degrees of relative concurrency and nondeterminism of processes.

Unifying Equivalences for Higher Dimensional Automata

The intention of the paper is to show how several categorical (open morphisms, path morphisms and coalgebraic morphisms based) approaches to an abstract characterization of bisimulation relate to each other and to behavioral bisimulations, in the setting of higher dimensional automata. Such a relating makes it possible to develop a metatheory designed for unified definition and study of equivalences in true concurrency semantics.

From Event-Oriented Models to Transition Systems

Two structurally different methods of associating transition system semantics to event-oriented models of distributed systems are distinguished in the literature. One of them is based on configurations (event sets), the other on residuals (model fragments). In this paper, a variety of models is investigated, ranging from extended prime event structures to configuration structures, and it is shown that the two semantics lead to isomorphic results. This strengthens prior work where bisimilarity (but not necessarily isomorphism) is achieved for a smaller range of models. Thanks to the isomorphisms obtained here, a wide range of facts known from the literature on configuration-based transition systems can be extended to residual-based ones.

Branching Processes of Timed Petri Nets

The intention of this note is to spread the Couvreur et al.’s semantic framework of branching processes [9], suitable for describing the behavior of general Petri nets with interleaving semantics, to timed general Petri nets with step semantics in order to characterize unfolding as the greatest element of a complete lattice of branching processes. In case of maximal step semantics of timed Petri nets, we impose some restrictions on the model behavior and define a new class of branching processes and unfoldings under the name of apt ones which are shown to satisfy the complete lattice properties.

A Domain View of Timed Behaviors

The intention of this paper is to introduce a timed extension of transition systems with independence, and to study its categorical interrelations with other time-sensitive models. In particular, we show the existence of a chain of coreflections leading from a category of the model of timed transition systems with independence to a category of a specially defined model of marked Scott domains. As an intermediate semantics we use a timed extension of occurrence transition systems with independence, able to properly capture causality and independence relations which arise in the presence of time delays.

A categorical view of timed weak bisimulation

Timed transition systems are a widely studied model for real-time systems The intention of the paper is twofold: first to show the applicability of the general categorical framework of open maps in order to prove that timed weak bisimulation is indeed an equivalence relation, and, second, to investigate how several categorical (open maps, path-bisimilarity and coalgebra based) approaches to an abstract characterization of bisimulation relate to each other and to timed weak bisimulation, in the setting of timed transition systems.