Homogeneous Semantics Preserving Deployments of Heterogeneous Networks of Embedded Systems

Abstract

Summary. Tagged systems provide a denotational semantics for embedded systems. A heterogeneous network of embedded systems can be modeled mathematically by a network of tagged systems. Taking the heterogeneous composition of this network results in a single, homogeneous, tagged system. The question this paper addresses is: when is semantics (behavior) preserved by composition? To answer this question, we use the framework of category theory to reason about heterogeneous system composition and derive results that are as general as possible. In particular, we define the category of tagged systems, demonstrate that a network of tagged systems corresponds to a diagram in this category and prove that taking the composition of a network of tagged systems is equivalent to taking the limit of this diagram-thus composition is endowed with a universal property. Using this universality, we are able to derive verifiable necessary and sufficient conditions on when composition preserves semantics.

On the Stability of Zeno Equilibria

“…Our investigations into the stability of Zeno equilibria are made possible through a categorical framework for hybrid systems (as first introduced in [9] and later utilized in [10]). This theory allows "non-hybrid" objects to be generalized to a hybrid setting.…”