Formal specification and verification of decentralized self-adaptive systems using symmetric nets

Engineering distributed self-adaptive systems is challenging due to multiple interacting components, some of which monitor and possibly modify the behavior of managed components that operate in highly dynamic settings. Formalizing such systems having a decentralized adaptation control has been recognized as a hard task. In this article, we introduce a formal framework based on Symmetric Nets (a well-established subclass of Colored Petri nets) for modeling and analyzing distributed self-adaptive discrete-event systems. Even though Petri Nets represent a sound and expressive formal model of concurrency and distribution, they cannot specify in a natural way structural changes enacted by adaptation procedures. We overcome this limitation by means of a two-layer modeling approach that enables clear separation of concerns and allows multiple decentralized adaptation procedures to be specified, validated, and verified against formal requirements. Validation and verification techniques are supported by powerful off-the-shelf tools tailored to Symmetric Nets. A self-healing manufacturing system case study is used to show applicability, advantages, and shortcomings of the approach. In particular, complexity issues are thoroughly discussed and mitigated by adopting complementary approaches based on interleaving reduction and behavioral symmetries exploitation.