Given a finite state system with partial observers and for each observer, a regular set of trajectories which we call a secret, we consider the question whether the observers can ever find out that a trajectory of the system belongs to some secret. We search for a regular control on the system, enforcing the specified secrets on the observers, even though… (More)
The paper generalizes the notion of a congruence on a category and pursues some of its applications. In particular, generalized congruences are used to provide a concrete construction of coequalizers in Cat. Extremal, regular and various other classes of epimorphic functors are characterized and interrelated .
Petri hypernets, a novel framework for modeling mobile agents based on nets-within-nets paradigm is presented. Hypernets employ a local and finitary character of interactions between agents, and provide means for a modular and hierarchical description. They are capable of modelling mobile agents tfrahat can dynamically change their hierarchy, and can… (More)
We present a model checking algorithm for alternating-time temporal logic (ATL) with imperfect information and imperfect recall. This variant of ATL is arguably most appropriate when it comes to modeling and specication of multi-agent systems. The related variant of model checking is known to be theoretically hard (∆ P 2-to PSPACE-complete, depending on the… (More)
The problem of finding a (functorial) concurrent realization of a reactive system by means of a labelled safe Petri net is studied. Firstly, a (functorial) construction is described that leads from the category of concrete asynchronous systems introduced by Morin to the category of labelled safe Petri nets. Then, the general problem is discussed. It is… (More)
Logics for expressing properties of Petri hypernets, a visual formalism for modelling mobile agents, are proposed. Two classes of properties are of interest—the temporal evolution of agents and their structural correlation. In particular, we investigate how the classes can be combined into a logic capable of expressing the dynamic evolution of the… (More)
The problem of finite completeness of categories of Petri nets is studied. Since Petri nets have finite products, the problem reduces to the issue of the existence of equalizers. We show that the categories of Petri nets with general and Winskel morphisms do not admit equalizers, and hence are not finitely complete. An important class of multiplicative… (More)