Sp X-Machines: Formal State-Based Modelling of Spatial Agents

Abstract

Applications of biological or biologically inspired multi-agent systems (MAS) often assume a certain level of reliability and robustness, which is not always straightforward. Formal modelling and verification of MAS may present many interesting challenges. For instance, formal verification may be cumbersome or even impossible to be applied on models with increased complexity. On the other hand, the behaviour of MAS consists of communities evolving in space and time (such as social insects, tissues, colonies of bacteria, etc.) which are characterised with a highly dynamic structure. In order to provide a neat and effective way to modelling and verification of these systems, we focus on their spatial characteristics. Spatial agents (i.e. agents distributed and moving through a physical space) can be modelled with X-machines – one of the most prominent formalisms for modelling the behaviour of biological colonies. However, it will be demonstrated that there are certain problems in the X-machines models, common to every spatial MAS. To overcome these disadvantages, we introduce an X-machines variation that besides facilitating formal modelling, will provide grounds towards visual animation of these systems. This approach resulted into a novel progression, Spatial X-machines ( sp XM), without retracting the legacy characteristics of X-machines such as testing and verification strategies. Finally, we present a supporting framework to modelling and verification of spatial multi-agent system, by utilizing the Spatial X-machines approach.