Abstract. This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.

Abstract. This paper aims to simplify recent efforts proposed by the Berkeley school in giving a formal semantics to the Ptolemy toolbox. We achieve this by developing a simple and elegant functional theory of deterministic tag systems that is a generalisation of Kahn Process Network theory (KPN). Our theory extends KPN by encompassing networks of processes labelled by tags from partially ordered sets and makes deeper use of Scott theory of Complete Partial Orders (CPO). Since CPO compose well under direct sums, heterogeneous systems are simply captured by direct sums of homogeneous systems, which are in turn constructed by connecting systems over different tag sets by means of tag conversion processes. For the (large) class of tag systems of “stream ” type, we show how to define tag conversion processes and how to implement process communication. The resulting architecture is fully decentralised and does not require Ptolemy’s directors. Last but not least, it provides distribution for free. 1