Signal set tissue systems and overlapping localities

In signal set tissue systems with overlapping localities (ssolt-systems) evolution rules can be associated with several cells. Rules may influence each other through instant signalling and, moreover, they are synchronised when sharing activated cells. The latter is a new feature. We study the behaviour of ssolt-systems in the form of labelled step transition systems. This allows to compare ssolt-systems with and without signalling and overlapping localities. Next the synthesis problem is considered, i.e., the question when given a step transition system, how to effectively construct an ssolt-system exhibiting this behaviour. To this end, ssolt-systems are related to a new class of Petri nets, that are behaviourally equivalent to ssolt-systems. It is shown how certain region based synthesis techniques can be applied to these nets and hence are also available for ssolt-systems.