3 research outputs found
String Diagrammatic Trace Theory
We extend the theory of formal languages in monoidal categories to the
multi-sorted, symmetric case, and show how this theory permits a graphical
treatment of topics in concurrency. In particular, we show that Mazurkiewicz
trace languages are precisely symmetric monoidal languages over monoidal
distributed alphabets. We introduce symmetric monoidal automata, which define
the class of regular symmetric monoidal languages. Furthermore, we prove that
Zielonka's asynchronous automata coincide with symmetric monoidal automata over
monoidal distributed alphabets. Finally, we apply the string diagrams for
symmetric premonoidal categories to derive serializations of traces.Comment: Paper accepted for MFCS 202