Marek A. Bednarczyk

Modelling mobility with petri hypernets

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 communicate with each other and with the outside world by exchanging messages, i.e., other mobile agents.

General Morphisms of Petri Nets (Extended Abstract)

A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of Petri nets is shown to admit products. Potential applications of general morphisms are indicated.

Modular system development with pullbacks

Two, seemingly different modular techniques for concurrent system development are investigated from a categorical perspective. A novel approach is presented in which they turn out to be merely special instances of pullback, a general categorical limit construction. Interestingly, the approach is based on truly concurrent semantics of systems.

On Concurrent Realization of Reactive Systems and Their Morphisms

The paper introduces the notion of concurrent realization of reactive systems. A framework is also presented in which labelled safe Petri nets as concurrent realizations of concrete asynchronous systems are constructed. The construction is uniform in the sense that it extends to a realization of arbitrary commuting diagrams. We discuss applicability of the framework to construct maximally concurrent realizations of reactive systems.

Synthesis and Verification of Uniform Strategies for Multi-agent Systems

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 specification of multi-agent systems. The related variant of model checking is known to be theoretically hard (\(\Delta^{\rm P}_{2}\)- to pspace-complete, depending on the assumptions), but virtually no practical attempts at it have been proposed so far. Our algorithm searches through the set of possible uniform strategies, utilizing a simple reduction technique. In consequence, it not only verifies existence of a suitable strategy but also produces one (if it exists). We validate the algorithm experimentally on a simple scalable class of models, with promising results.

Finite Completeness of Categories of Petri Nets

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. The main positive result of the paper states that reachable Petri nets with multiplicative morphisms form a finitely complete category. As an application of this result, some well-known categories are shown to be finitely complete. For instance, since all morphisms between reachable safe Petri nets are multiplicative, it follows that the category of reachable safe Petri nets is finitely complete.

Bayesian Network Mining System

The paper provides an exhaustive description of a new system serving learning, viewing and reasoning with Bayesian networks.

Model Checking Properties of Multi-agent Systems with Imperfect Information and Imperfect Recall

The problem of practical model checking Alternating-time Temporal Logic (ATL) formulae under imperfect information and imperfect recall is considered. This is done by synthesis and subsequent verification of strategies, until a good one is found. To reduce the complexity of the problem we define an equivalence relation on strategies. Then an algorithm for model checking a class of modal properties with a single coalitional modality is presented, which utilises the observation that there is no need to verify more than one strategy from an equivalence class. The experimental results of the approach are also discussed.

Modelling and Analysing Systems of Agents by Agent-Aware Transition Systems

We propose a method to specify, in a modular way, complex systems formed by interacting agents. The method is based on the notion of view, that is a partial representation of the system, reflecting one of its specific aspects. By composing the different views, we get the overall system, described as a special kind of transition system. By means of a suitable logical language, we can express interesting properties of the system; model-checking techniques can then be used to assess their validity. Views can be specified using different languages or notations, provided they can be translated in so-called agent aware transition systems. The method is explained with the help of a simple, but non trivial example.

SMC: synthesis of uniform strategies and verification of strategic ability for multi-agent systems

We present a model checking algorithm for a subset of 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 specification of multi-agent systems. The related variant of model checking is known to be theoretically hard (NPto PSPACE-complete, depending on the assumptions), but very few practical attempts at it have been proposed so far. Our algorithm searches through the set of possible uniform strategies, utilizing a simple technique that reduces the search space. In consequence, it does not only verify existence of a suitable strategy but also produces one (if it exists). We validate the algorithm experimentally on a simple scalable class of models, with promising results. We also discuss two variants of the model checking problem, related to the objective vs. subjective interpretation of strategic ability. We provide algorithms for reductions between the two semantic variants of model checking. The algorithms are experimentally validated as well.