Commutation Preperties and Generating Sets Characterize Slices of Various Synchronization Primitives

Abstract Various synchronization primitives are described by adding and testing integer vectors, or by using “Petri Nets”. A slice represents a local behavior, described by permissible sequences of distinct actions of the system. We present a double characterization of slices defined by various synchronization primitives: In terms of generating sets and dually in terms of commutation properties. A typical form of a commutation property is: The set of sequences of past actions which disallow a certain coming action is closed under certain permutations. The synchronization primitives treated here include various systems which lie between PV and Vector Replacement Systems or Petri Nets.