Non-smooth and zeno trajectories for hybrid system algebra

Hybrid systems are heterogeneous systems characterised by the interaction of discrete and continuous dynamics. In this paper we compare a slightly extended version of our earlier algebraic approach to hybrid systems with other approaches. We show that hybrid automata, which are probably the standard tool for describing hybrid systems, can conveniently be embedded into our algebra. But we allow general transition functions, not only smooth ones. Moreover we embed other models and point out some important advantages of the algebraic approach. In particular, we show how to easily handle Zeno effects, which are excluded by most other authors. The development of the theory is illustrated by a running example and a larger case study

10271 Abstracts Collection -- Verification over discrete-continuous boundaries

From 4 July 2010 to 9 July 2010, the Dagstuhl Seminar 10271 ``Verification over discrete-continuous boundaries\u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Labelled transition systems as a Stone space

A fully abstract and universal domain model for modal transition systems and refinement is shown to be a maximal-points space model for the bisimulation quotient of labelled transition systems over a finite set of events. In this domain model we prove that this quotient is a Stone space whose compact, zero-dimensional, and ultra-metrizable Hausdorff topology measures the degree of bisimilarity such that image-finite labelled transition systems are dense. Using this compactness we show that the set of labelled transition systems that refine a modal transition system, its ''set of implementations'', is compact and derive a compactness theorem for Hennessy-Milner logic on such implementation sets. These results extend to systems that also have partially specified state propositions, unify existing denotational, operational, and metric semantics on partial processes, render robust consistency measures for modal transition systems, and yield an abstract interpretation of compact sets of labelled transition systems as Scott-closed sets of modal transition systems.Comment: Changes since v2: Metadata updat

Dagstuhl News January - December 2006

"Dagstuhl News" is a publication edited especially for the members of the Foundation "Informatikzentrum Schloss Dagstuhl" to thank them for their support. The News give a summary of the scientific work being done in Dagstuhl. Each Dagstuhl Seminar is presented by a small abstract describing the contents and scientific highlights of the seminar as well as the perspectives or challenges of the research topic

Continuum percolation theory of epimorphic regeneration

A biophysical model of epimorphic regeneration based on a continuum percolation process of fully penetrable disks in two dimensions is proposed. All cells within a randomly chosen disk of the regenerating organism are assumed to receive a signal in the form of a circular wave as a result of the action/reconfiguration of neoblasts and neoblast-derived mesenchymal cells in the blastema. These signals trigger the growth of the organism, whose cells read, on a faster time scale, the electric polarization state responsible for their differentiation and the resulting morphology. In the long time limit, the process leads to a morphological attractor that depends on experimentally accessible control parameters governing the blockage of cellular gap junctions and, therefore, the connectivity of the multicellular ensemble. When this connectivity is weakened, positional information is degraded leading to more symmetrical structures. This general theory is applied to the specifics of planaria regeneration. Computations and asymptotic analyses made with the model show that it correctly describes a significant subset of the most prominent experimental observations, notably anterior-posterior polarization (and its loss) or the formation of four-headed planaria.Comment: This author wish to retract the paper arXiv:1705.06720 because it began as part of a collaboration that later fell apart and it was published without the consent from the collaborators. Furthermore, the collaborators have managed to provide a better solution to this proble

Coalgebra for the working software engineer

Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems