This work investigates the axiomatic concurrency theory proposed by Carl Adam Petri as a basis of general net theory starting with physically motivated axioms. A formulation in terms of partially ordered sets is intensionally not adopted here, in order to deal with this theory in a more general setting, viewing causality and concurrency as pure similarity relations. Concurrency structures, which are the models of this theory, are intended to describe the synchronisation structure of possibly cyclic processes at an arbitrary level of abstraction.

The major result of this work is that under certain conditions we can associate exactly two nets (of which one is the inverse of the other) with every concurrency structure. An appropriate elementary-net-specification based upon one of these nets has a case class that coincides with the class of statelike cuts. In other words, under appropriate assumptions supplementing Petri's axioms the token game is sound and complete to evolve the dynamics of concurrency structures.