Complexity results for 1-safe nets

Allan Cheng, Javier Esparza, Jens Palsberg
1995 Theoretical Computer Science  
We study the complexity of several standard problems for l-safe Petri nets and some of its subclasses. We prove that reachability, liveness, and deadlock are all PSPACE-complete for l-safe nets. We also prove that deadlock is NP-complete for free-choice nets and for l-safe free-choice nets. Finally, we prove that for arbitrary Petri nets, deadlock is equivalent to reachability and liveness. . 'Work done while this author was at the University of Edinburgh. 0304-3975/95/%09.50 0 1995-Elsevier
more » ... ence B.V. All rights reserved SSDI 0304-3975(94)00231-2 118 A. Cheng et al. / Theoretical Computer Science 147 (1995) 117-136 however difficult to extend to Place/Transition nets. Nielsen, Rozenberg and Thiagarajan [33, 28] have shown that a model of l-safe nets, called Elementary Net Systems, has strong categorical connections with many other models of concurrency, such as event structures (another good reference is [35] ). Finally, l-safe nets are closer to classical language theory, and can be interpreted as a synchronisation of finite automata. These properties have motivated the design of verification methods particularly suited for l-safe nets. The obvious connection to Mazurkiewicz trace theory [26, 35] has been exploited to design efficient "partial-order" verification methods [34, 14].
doi:10.1016/0304-3975(94)00231-7 fatcat:tgp7u5pvhze4fbyupzvbj72yau