Shape Calculus: Timed Operational Semantics and Well-formedness

TL;DR

The paper introduces a formal timed operational semantics for the Shape Calculus, a bio-inspired framework for modeling 3D shapes and their interactions, including collision, binding, and splitting, with applications in biological scenarios.

Contribution

It provides the complete formal timed semantics of the Shape Calculus and proves well-formedness of evolving networks of 3D processes.

Findings

Formal timed semantics of the calculus is established.

Examples demonstrate biological applications.

Well-formedness of process networks is proven.

Abstract

The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel that models naturally binding sites on the surface of shapes. Processes can represent molecules or other mobile objects and can be part of networks of processes that move simultaneously and interact in a given geometrical space. The calculus embeds collision detection and response, binding of compatible 3D processes and splitting of previously established bonds. In this work the full formal timed operational semantics of the calculus is provided, together with examples that illustrate the use of the calculus in a well-known biological scenario. Moreover, a result of well-formedness about the evolution of a given network of well-formed 3D processes is proved.