In: J.-M. Colom, M. Koutny (Eds.), Newcastle upon Tyne, UK: Proc. of 22nd International Conf. on Applications and Theory of Petri Nets 2001 (ICATPN 2001), pages 184-203. Lecture Notes in Computer Science 2075, edited by G. Goos, J. Hartmanis and J. van Leuwen, Springer, June 2001.
Abstract: This paper presents new results concerned with liveness, liveness of a subset of transitions and deadlock in Petri nets. Liveness is seen as a particular case of what we call T-liveness: all transitions in the set T are live. The first results characterize the relation between supervisors enforcing liveness and T-liveness with supervisors preventing deadlock. Then we introduce a class of Petri net subnets allowing us to extend two well known results. Specifically we generalize the result relating deadlock to siphons and the extension to asymmetric choice Petri nets of the Commoner's Theorem. We conclude by considering how the theoretical results of this paper can be used for deadlock prevention, least restrictive deadlock prevention and least restrictive T-liveness enforcement. Keywords liveness, deadlock, synthesis of liveness supervisors, structural properties of Petri nets.