Shape Calculus: Timed Operational Semantics and Well-formedness

The Shape Calculus is a bio-inspired calculus for describing 3Dshapes moving in a space. A shape forms a 3D process when combinedwith a behaviour. Behaviours are specified with a timed CCS-like pro-cess algebra using a notion of channel that models naturally bindingsites on the surface of shapes. Processes can represent molecules orother mobile objects and can be part of networks of processes thatmove simultaneously and interact in a given geometrical space. Thecalculus embeds collision detection and response, binding of compati-ble 3D processes and splitting of previously established bonds. In thiswork the full formal timed operational semantics of the calculus is pro-vided, together with examples that illustrate the use of the calculus ina well-known biological scenario. Moreover, a result of well-formednessabout the evolution of a given network of well-formed 3D processes isproved.