<tdalign="left"><i><u>Uli Fahrenberg</u>, Christian Johansen, Georg Struth, Krzysztof Ziemiański</i></td>
<tdalign="left"><i><u>Uli Fahrenberg</u>, Christian Johansen, Georg
Struth and Krzysztof Ziemiański</i></td>
<tdalign="left",width="60%">
<ahref="javascript:toggleDiv('T43')">Languages of Higher-Dimensional Automata (short talk)</a>
<divstyle="display:none",id="T43"><br/><br/>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 a notion of event consistency. HDAs are then finite, labeled, event-consistent precubical sets with distinguished subsets of initial and accepting cells. Their languages are sets of interval orders closed under subsumption; as a major technical step we expose a bijection between interval orders and a subclass of HDAs. We show that any finite subsumption-closed set of interval orders is the language of an HDA, that languages of HDAs are closed under binary unions and parallel composition, and that bisimilarity implies language equivalence.