Constructive Potential Theory: Foundations and Applications.

Stochastic analysis is now an important common part of computing and mathematics. Its applications are impressive, ranging from stochastic concurrent and hybrid systems to finances and biomedicine. In this work we investigate the logical and algebraic foundations of stochastic analysis and possible applications to computing. We focus more concretely on functional analysis theoretic core of stochastic analysis called potential theory. Classical potential theory originates in Gauss and Poincare's work on partial differential equations. Modern potential theory now study stochastic processes with their adjacent theory, higher order differential operators and their combination like stochastic differential equations. In this work we consider only the axiomatic branches of modern potential theory, like Dirichlet forms and harmonic spaces. Due to the inherently constructive character of axiomatic potential theory, classical logic has no enough ability to offer a proper logical foundation. In this paper we propose the weak commutative linear logics as a logical framework for reasoning about the processes described by potential theory. The logical approach is complemented by an algebraic one. We construct an algebraic theory with models in stochastic analysis, and based on this, and a process algebra in the sense of computer science. Applications of these in area of hybrid systems, concurrency theory and biomedicine are investigated. Parts of this paper have been presented, in shorter form, at diverse conferences and workshops. This work represents a common 'umbrella' for all these presentations and offers an extended version for the (some time) very short published materials

An Integrated Specification Framework for Embedded Systems

In this paper, we address the complex issue of representation of continuous behaviour of the environment of the embedded controllers. In our approach we propose two novel ideas. One is to consider the weak solutions to describe the evolutions of the dynamical systems. The second novelty is to make available, at the design stage, the information about concurrent evolutions of the environment. We propose a new logic called the Hilbertean logic for representing continuous behaviours. Then, we use the causal order relations to integrate this logic with a probabilistic process algebra. For the resulting specification framework, we construct a denotational semantics rich in mathematical properties

Towards co-engineering communicating autonomous cyber-physical systems

In this paper, we sketch a framework for interdisciplinary modeling of space systems, by proposing a holistic view. We consider different system dimensions and their interaction. Specifically, we study the interactions between computation, physics, communication, uncertainty and autonomy. The most comprehensive computational paradigm that supports a holistic perspective on autonomous space systems is given by cyber-physical systems. For these, the state of art consists of collaborating multi-engineering efforts that prompt for an adequate formal foundation. To achieve this, we propose a leveraging of the traditional content of formal modeling by a co-engineering proces

The practice turn in organisational studies and construction management research

In this work, we address the issue of handling complex continuous evolutions of the environment of embedded systems. There is now an impressive amount of research in the area of intelligent embedded controllers, and thus we do not need to argue about the importance of this subject

Co-evolution preserving model reduction for uncertain cyber-physical systems - towards a framework for nanoscience

In Joaquim Filipe, Juan Andrade-Cetto, Jean-Louis Ferrier, editors, ICINCO 2009, Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and Control, Milan, Italy, July 2-5, 2009. pages 39-46, INSTICC Press, 2009

Bisimulation, logic and mobility for Markovian systems

Nowadays, anyone can easily observe an explosive development in distributed embedded systems like sensor networks, gene regulatory networks and other system biology areas. A general tendency in this development is the integration of different features, like mobility, randomness, continuity and discrete/continuous mixed behaviors. In this paper, we present two formal mechanisms for developing a formal framework, in which these various features can be investigated altogether. One mechanism represents a unifying axiomatization of deterministic and stochastic automata, in the spirit of the recently introduced paradigm called Hilbertian formal methods [6]. The second one proposes a generic technique based on the categorical domain theory for adding new features to an existing model. This mechanism constitutes a formal approach to a recent development paradigm called multi-dimensional codesign [5]. In the limited space of this paper, we restrict our presentation to a class of systems that mix continuous evolutions with logical mobility

A coordination model for ultra-large scale systems of systems

The ultra large multi-agent systems are becoming increasingly popular due to quick decay of the individual production costs and the potential of speeding up the solving of complex problems. Examples include nano-robots, or systems of nano-satellites for dangerous meteorite detection, or cultures of stem cells for organ regeneration or nerve repair. The topics associated with these systems are usually dealt within the theories of intelligent swarms or biologically inspired computation systems. Stochastic models play an important role and they are based on various formulations of the mechanical statistics. In these cases, the main assumption is that the swarm elements have a simple behaviour and that some average properties can be deduced for the entire swarm. In contrast, complex systems in areas like aeronautics are formed by elements with sophisticated behaviour, which are even autonomous. In situations like this, a new approach to swarm coordination is necessary. We present a stochastic model where the swarm elements are communicating autonomous systems, the coordination is separated from the component autonomous activity and the entire swarm can be abstracted away as a piecewise deterministic Markov process, which constitutes one of the most popular model in stochastic control. Keywords: ultra large multi-agent systems, system of systems, autonomous systems, stochastic hybrid systems