Trace spaces of directed tori with rectangular holes

In [4] the trace space of parallel non-looped, non-branching processes is given as a prod-simplicial complex derived from an index category. For looped processes, the state space is a torus and the trace space is a disjoint union of tracespaces of deloopings. The index category for the trace space of the deloopings is developed from the once delooped case. When just one process is looped, the index category is generated as words in a regular language. The automaton is constructed.