The approach to process semantics using quantales and modules is topologized by considering tropological systems whose sets of states are replaced by locales and which satisfy a suitable stability axiom. A corresponding notion of localic suplattice (algebra for the lower powerlocale monad) is described, and it is shown that there are contravariant functors from sup-lattices to localic sup-latic...

The algebraic approach to formal language and automata theory is a continuation of the earliest traditions in these fields which had sought to represent languages, translations and other computations as expressions (e.g. regular expressions) in suitably-defined algebras; and grammars, automata and transitions as relational and equational systems over these algebras, that have such expressions a...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

Hybrid systems are heterogeneous systems characterised by the interaction of discrete and continuous dynamics. We present a trajectory-based algebraic model for describing hybrid systems; the trajectories used are closely related to streams. The algebra is based on left quantales and left semirings and provides a new application for these algebraic structures. We show that hybrid automata, whic...