Abstract
It has been a hot research topic to synthesize maximally permissive controllers with fewest monitors. So far, all maximally permissive control models for a well-known benchmark are generalized Petri net, which com-plicates the system. In addition, they all relied on time-consuming reachability analysis. Uzam and Zhou ap-ply First-met-bad-marking (FBM) method to the benchmark to achieve a near maximal permissive control policy with the advantage of no weighted control (WC) arcs. To improve the state of the art, it is interesting to synthesize optimal controller with as few weighted arcs as possible since it is unclear how to optimize the control for siphon involving WC arcs, This paper explores the condition to achieve optimal controller with-out WC and defining a new type of siphon, called α-siphon. If the condition is not met, one can apply the technique by Piroddi et al. to synthesize optimal controllers with WC.
Highlights
Petri nets are a popular and powerful formalism to handle deadlock problems in a resource allocation system that is a technical abstraction of contemporary technical systems
All maximally permissive control models for a well-known benchmark are generalized Petri net, which complicates the system. They all relied on time-consuming reachability analysis
To improve the state of the art, it is interesting to synthesize optimal controller with as few weighted arcs as possible since it is unclear how to optimize the control for siphon involving weighted control (WC) arcs, This paper explores the condition to achieve optimal controller without WC and defining a new type of siphon, called α-siphon
Summary
Petri nets are a popular and powerful formalism to handle deadlock problems in a resource allocation system that is a technical abstraction of contemporary technical systems. Reaching 19 states fewer and 6 more monitors than that the optimal one by Piroddi et al for a well-known benchmark, it does not employ weighted control arcs and runs more efficiently. Mixture siphons containing nonsharing resource places may be emptiable This method does not need to enumerate all minimal siphons, nor to compute the reachability graph. An earlier paper helps this by proposing one way to list all lost states and estimating the number of lost states without reachability analysis Analyzing these state losses, one may find some enhancements to reach more states. If no more states can be reached, one stop and satisfy with the suboptimal model obtained or to employ weighted control arcs to reach more states following the approach by Piroddi et al. The rest of the paper is organized as follows.
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