4 citations · 4 across the 5 of their papers we have counts for
9 papers
Track objects in cubical presheaf automata
Georg Struth, Krzysztof Ziemiański
Using the formalism of presheaf automata, we introduce new classes of automata for modelling concurrency that extend higher-dimensional automata and symmetric higher-dimensional au…
Myhill-Nerode Theorem for Higher-Dimensional Automata
Uli Fahrenberg, Krzysztof Ziemiański
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 stand…
Generating Posets with Interfaces
Olavi Äikäs, Uli Fahrenberg, Christian Johansen +1
We generate and count isomorphism classes of gluing-parallel posets with interfaces (iposets) on up to eight points, and on up to ten points with interfaces removed. In order to do…
Kleene Theorem for Higher-Dimensional Automata
Uli Fahrenberg, Christian Johansen, Georg Struth +1
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…
Configuration spaces and directed paths on the final precubical set
Jakub Paliga, Krzysztof Ziemiański
The main goal of this paper is to prove that the space of directed loops on the final precubical set is homotopy equivalent to the "total" configuration space of points on the plan…
Languages of Higher-Dimensional Automata
Uli Fahrenberg, Christian Johansen, Georg Struth +1
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 isom…
Spaces of directed paths on pre-cubical sets II
Krzysztof Ziemiański
For a given pre-cubical set (--set) with two distinguished vertices $\bO$, $\bI$, we prove that the space $\vP(K)_\bO^\bI$ of d-paths on the geometric realization of $…
Paths of the directed suspension
Andrzej Weber, Krzysztof Ziemiański
We prove that the loop space of the directed suspension of a directed space is homotopy equivalent to the James construction. In particular, it does not depend on the directed stru…
Homotopy representations of the unitary groups
Wojciech Lubawski, Krzysztof Ziemiański
Let be a compact connected Lie group and let be complex vector bundles over the classifying space . The problem we consider is whether contains a subbundle which…