Tag Machines

We present an extension of a mathematical framework proposed by the authors to deal with the composition of heterogeneous reactive systems. Our extended framework encompasses diverse models of computation and communication such as synchronous, asynchronous, causality-based partial orders, and earliest execution times. We introduce an algebra of tag structures and morphisms between tag sets to define heterogeneous parallel composition formally and we use a result on pullbacks from category theory to handle properly the case of systems derived by composing many heterogeneous components. The extended framework allows us to establish theorems, from which design techniques for correct-by-construction deployment of abstract specifications can be derived. We illustrate this by providing a complete formal support for correct-by-construction distributed deployment of a synchronous design specification over a medium of LTTA type (Loosely Time-Triggered Architecture).

Keywords : reactive systems, embedded systems, synchronous, asynchronous, GALS, formal methods, heterogeneous systems.