On liveness and boundedness of asymmetric choice nets

Abstract

This paper concerns two important techniques, characterization and property-preserving transformation, for verifying some basic properties of asymmetric choice Petri nets (AC nets). In the literature, a majority of the characterizations are for ordinary free choice nets. This paper presents many extended (from free choice nets) and new characterizations for four properties: liveness with respect to an initial marking, liveness monotonicity with respect to an initial marking, well-formedness, liveness and boundedness with respect to an initial marking. The nets involved are extended to homogeneous free choice nets, ordinary AC nets and homogeneous AC nets. This paper also investigates the transformation of merging a set of places of an ordinary AC net and proposes the conditions for it to preserve the siphon-trap-property (ST-property), liveness, boundedness and reversibility. The results are then applied to the verification of resource-sharing systems. At present, the major approaches for solving this problem are based on state machines or marked graphs and are not based on property preservation. Our approach extends the scopes of the underlying nets to AC nets and the verification techniques. It is found that the ST-property plays a very important role in many of the results. Furthermore, mainly through examples, the importance of the assumptions in the proposed characterizations and transformation and the limitation on further extensions are pointed out.