• A Kleene Theorem for Higher-Dimensional Automata 

      Fahrenberg, Uli; Johansen, Christian; Struth, Georg; Ziemiański, Krzysztof (Peer reviewed; Journal article, 2022)
      We prove a Kleene theorem for higher-dimensional automata (HDAs). It states that the languages they recognise are precisely the rational subsumption-closed sets of interval pomsets. The rational operations include a gluing ...
    • Languages of higher-dimensional automata 

      Fahrenberg, Uli; Johansen, Christian; Struth, Georg; Ziemiański, Krzysztof (Journal article; Peer reviewed, 2021)
      We introduce languages of higher-dimensional automata (HDAs) and develop some of their properties. To this end, we define a new category of precubical sets, uniquely naturally isomorphic to the standard one, and introduce ...
    • Sculptures in concurrency 

      Fahrenberg, Uli; Johansen, Christian; Trotter, Christopher A.; Ziemiański, Krzysztof (Peer reviewed; Journal article, 2021)
      We give a formalization of Pratt's intuitive sculpting process for higher-dimensional automata (HDA). Intuitively, an HDA is a sculpture if it can be embedded in (i.e., sculpted from) a single higher dimensional cell ...