An Incremental Approach to Extracting Minimal Bad Siphons

Abstract

Finding all minimal bad siphons is essential for deadlock control. However, the number of siphons grows exponentially with the size of the system. Deadlock occurs due to inappropriate resource sharing. Hence most research focused on the problem of minimal siphon extraction covering a set of places representing resources — an NP-Complete problem for arbitrary Petri Nets. We develop the theory for efficient extraction of minimal bad siphons for S3PR (systems of simple sequential processes) proposed by Ezpeletaet al. The number of minimal bad siphons that needs to be searched is linear to the number of resources. The rest can be found by adding and deleting common sets of places from existing ones significantly reducing the search time. It is very interesting that both nets and siphons can be synthesized by first locating a circuit followed by adding handles.