Characterizing Behavioural Congruences for Petri Nets

We exploit a notion of interface for Petri nets in order to design a set of net combinators. For such a calculus of nets, we focus on the behavioural congruences arising from four simple notions of behaviour, viz., traces, maximal traces, step, and maximal step traces, and from the corresponding four notions of bisimulation, viz., weak and weak step bisimulation and their maximal versions. We characterize such congruences via universal contexts and via games, providing in such a way an understanding of their discerning powers

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Petri-net-based 2D Design of DNA Walker Circuits

We consider localised DNA computation, where a DNA strand walks along a binary decision graph to compute a binary function. One of the challenges for the design of reliable walker circuits consists in leakage transitions, which occur when a walker jumps into another branch of the decision graph. We automatically identify leakage transitions, which allows for a detailed qualitative and quantitative assessment of circuit designs, design comparison, and design optimisation. The ability to identify leakage transitions is an important step in the process of optimising DNA circuit layouts where the aim is to minimise the computational error inherent in a circuit while minimising the area of the circuit. Our 2D modelling approach of DNA walker circuits relies on coloured stochastic Petri nets which enable functionality, topology and dimensionality all to be integrated in one two-dimensional model. Our modelling and analysis approach can be easily extended to 3-dimensional walker systems

A Fast Hybrid Color Segmentation Method

. We introduce a very general method of achieving stable and fast color segmentation. This method works on different hierarchical data structures and combines local bottom-up region growing segmentation with top-down separation techniques. As our method supports exploitation of inherent parallelism, a real-time object detection has been designed and is in the implementation phase. 1 Introduction Image segmentation is an important step towards an object detection in image analysis. In the literature several major methods for segmentation are distinguished [4]. Common are edge-detection, region-growing and clustering techniques. Whilst clustering uses mainly statistical methods, syntactical methods are more popular for edge-detection and region-growing techniques. Regiongrowing methods are usually classified as local, global or splitting-and-merging techniques. Local techniques are simple and fast, but have the problem of chaining: two very dissimilar pixels may be connected by a chain..

Reducing k-safe Petri Nets to Pomset-equivalent 1-safe Petri Nets

It is a well-known fact that for every k-safe Petri net, i.e. a Petri net in which no place contains more than k $\in$ N tokens under any reachable marking, there is a 1-safe Petri net with the same interleaving behaviour. Indeed these types of Petri nets generate regular languages. In this paper, we show that this equivalence of k-safe and 1-safe Petri nets holds also for their pomset languages, a true-concurrency semantics. Keywords: Causality / partial order theory of concurrency, Petri nets, Pomsets

Abstract fairness and semantics

Fairness of a program execution, c, usually expresses that all objects which are sufficiently often enable have to occur also sufficiently often in c. There exists a well-known strong equivalence between fair program executions, #PI#_3"0-formulae, and convergence of initial program executions. However, these results cannot be applied to a study of 'fair semantics' of programs, as such a fair semantics is a #SIGMA#_1"1-formula in general. The main reason therefore is that a semantics does not tell which objects are enabled - only the actually occurring objects are usually seen in semantics. Here we study on a very abstract level some quite natural requirements for semantics s.t. fair semantics with invisible 'enabledness' can also be characterized with topological techniques. (orig.)Available from TIB Hannover: RO 6844(1995,16) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman