A Partial Order Semantics for FIFO-Nets

In this work, we give a true concurrency semantics for FIFO-nets, that are Petri nets in which places behave as queues, tokens take values in a finite alphabet and the firing of a transition depends on sequences on the alphabet. We introduce fn-processes to represent the concurrent behavior of a FIFO-net N during a sequence of transition firings. Fn-processes are modeled by a mapping from a simple FIFO-net without queue sharing and cycles, named FIFO-occurrence net, to N. Moreover, the relation among the firings expressed by the FIFO-occurrence net has been enriched by an ordering relation among the elements of the FIFO-occurrence net representing values entered into a same queue of N. We give a way to build fn-processes step by step in correspondance with a sequence of transition firings and the fn-processes operationally built are all those abstractly defined. The FIFO-occurrence nets of fn-processes have some interesting properties; for example, such nets are always discrete and, consequently, there is at least a transition sequence corresponding to each fn-process.