Net-based control versus rational control The relation between ITNC vector languages and rational relations

Abstract.

 An Individual Token Net Controller (or ITNC) is a particular type of state-machine decomposable Petri net that can be used as a synchronization mechanism in concurrent systems consisting of a fixed number of sequential subsystems. In this paper the family of ITNC vector languages is compared to the well-known family of rational relations. On the one hand it is proved that the family of rational relations equals the family of vector languages of Generalized ITNCs, i.e. ITNCs in which the restriction of completeness is dropped. On the other hand a vector language property induced by completeness is identified that precisely characterizes the difference between ITNC vector languages and Generalized ITNC vector languages. In addition, the results are shown to carry over to the prefix-closed versions of the models.