Structural Liveness Analysis of Automated Manufacturing Systems Modeled by S4PRs

This paper presents a liveness analysis method for sequential automated manufacturing systems (AMSs), which can be modeled by a class of Petri nets named systems of sequential systems with shared resources (S
⁴
PR). We show that deadlocks in S
⁴
PR can be characterized by the saturation of its structural object named a perfect activity circuit (PA-circuits). Thus, S
⁴
PR is live if and only if no PA-circuits in it is saturated at all reachable states. A PA-circuits of an S
⁴
PR may not be saturated at any state; hence, we propose an integer linear program (ILP) to determine whether a PA-circuits can be saturated or not. Then an algorithm is proposed to compute the set of PA-circuits that may be saturated. This presented method nontrivially generalizes deadlock characterization and liveness condition of ordinary Petri nets to a broader class of nonordinary ones.