Synthesis of liveness enforcing supervisory policies in Petri nets by stepwise refinement

The refinement procedure of Suzuki and Murata [1] combines two Petri Nets (PNs) N₁(m⁰₁) and N₂(m⁰₂) in a prescribed manner to obtain a PN N₃(m⁰₃). Under appropriate conditions, the liveness of the PNs N₁(m⁰₁) and N₂(m⁰₂) implies the liveness of the PN N₃(m⁰₃). A PN that is not live, can be made live by a liveness enforcing supervisory policy (LESP). In this paper, we develop the results of Suzuki and Murata to yield a class of PNs for which an LESP for N₃(m⁰₃) can be represented in terms of local-LESPs for N₁(m⁰₁) and N₂(m⁰₂).