We prove a Kleene theorem for higher-dimensional automata. It states that the languages
they recognise are precisely the rational subsumption-closed sets of finite interval pomsets …

We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating
that a language is regular if and only if it has finite prefix quotient. HDAs extend standard …

In this paper we study finite higher-dimensional automata (HDAs) from the logical point of
view. Languages of HDAs are sets of finite bounded-width interval pomsets with interfaces …

In this paper we develop the language theory of higher-dimensional automata (HDAs).
Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) …

We introduce regular languages of morphisms in free monoidal categories, with their
associated grammars and automata. These subsume the classical theory of regular …

We introduce posets with interfaces (iposets) and generalise their standard serial
composition to a new gluing composition. In the partial order semantics of concurrency …

We introduce a new formalism of higher-dimensional timed automata, based on Pratt and
van Glabbeek's higher-dimensional automata and Alur and Dill's timed automata. We prove …

We introduce regular languages of morphisms in free monoidal categories, with their
associated grammars and automata. These subsume the classical theory of regular …

Interval-order partially ordered multisets with interfaces (ipomsets) have shown to be a
versatile model for executions of concurrent systems in which both precedence and …

We present a new language semantics for real-time concurrency. Its operational models are
higher-dimensional timed automata (HDTAs), a generalization of both higher-dimensional …