A Polynomial-Time Graph Algorithm to Decide Liveness of Some Basic Classes of Bounded Petri Nets

This paper is related to structural analysis of Petri nets where liveness and boundedness issues are addressed through the analysis of the combinatorial properties of the underlying graph. We first recall a number of basic results about liveness and boundedness involving combinatorial substructures (deadlocks and traps). It is then shown that testing whether a bounded Extended Free Choice net or a Non Self-Controlling net is structurally live can be reduced to the search for a strongly connected deadlock which is not a trap. This problem, in turn, is shown to be solvable in polynomial time through a purely combinatorial algorithm making combined use of Tarjan's strong connectivity algorithm and Minoux's LTUR algorithm for solving Horn satisfiability problems. Once structural liveness has been proved, testing liveness for a given initial marking is already known to be polynomially solvable.