On the deadlock analysis of multithreaded control software

Abstract

The long interest in finding efficient solutions to deadlock occurrence induced by resource sharing is persistent in the context of concurrent control software production. Petri net-based correction techniques which were traditionally applied in the context of flexible manufacturing systems (FMS) constitute a promising new approach. In this vein, Gadara nets were introduced as an attempt to import the strengths of these techniques into the software domain. In this paper, we prove that these Petri nets are close to a subclass of S 4 PR (a widely-exploited class in the context of FMS) and provide some related equivalence results. Some limitations which Gadara nets present for the modelling and automated correction of software are also unveiled. Last but no least, we present formal proofs of the theorems characterising non-liveness in Gadara nets. To our knowledge, no such proofs were published before.

On the Complexity of Some State-Counting Problems for Bounded Petri Nets

“…The result of Proposition 2 is well known to the relevant community and, therefore, its proof is omitted; a relevant formal argument can be found, for instance, in [9]. On the other hand, the significance of Proposition 2 for the needs of the undertaken analysis is revealed by the next corollary; this corollary results immediately when combining Proposition 2 with Proposition 1 and the discussion that precedes this second proposition in Section II-A.…”

“…Finally, the specification of the net N G is completed by specifying its initial marking M 0 by setting M 0 (p) = 0, for every p ∈ P S , M 0 (r) = 1, for every r ∈ P R , and M 0 (p 0 ) = |V |. 9 Such vertices are characterized as "zero-degree".…”

The deadlock problem in the control of Flexible Manufacturing Systems: An overview of the Petri net approach

“…One of these Petri net subclasses is that of Gadara nets [50]; a class originally conceived for studying the RAP in multithreaded software systems. However, all conflicts in the process paths of a Gadara net are resource-independent; a deficiency we have already approached from a critical position [36,34].…”

“…Relations within the S n PR family S 4 PR is the most general RAS net class for which, being defined with actual modelling needs of FMSs in mind, a full analysis theory has been developed. Besides, it can be seen as a superclass for many other models arising from diverse application domains [45,2,36,29]. The condition of superclass may directly derive from the structure [45] or being inferrable by simulating the evolution of behaviour through S 4 PR nets [36].…”