Marking homothetic monotonicity and fluidization of untimed Petri nets

The analysis of Discrete Event Systems suffer from the well known state explosion problem. A classical technique to overcome this problem is to relax the behaviour by partially removing the integrality constraints, thus dealing with hybrid or continuous systems. In the Petri nets framework, continuous net systems (technically hybrid systems) are the result of removing the integrality constraint in the firing of transitions. This relaxation may highly reduce the complexity of analysis techniques but may not preserve important properties of the original system. This paper deals with the basic operation of fluidization. More precisely, it aims at establishing conditions that a discrete system must satisfy so that a given property is preserved by the continuous system. These conditions will be mainly based on the here introduced marking homothetic behaviours of the system. The focus will be on logical properties as boundedness, deadlock-freeness, liveness and reversibility. Furthermore, testing homothetic monotonicity of some properties in the discrete systems will be considered.