Context-Based Behavioral Equivalence of Components in Self-Adaptive Systems

An important challenge to realize dynamic adaptation is finding suitable components for substitution or interaction according to the current context. A possible solution is checking behavioral equivalence of components in different contexts. Two components are equivalent with respect to a context, if they behave equivalently in that context. In this work, we deal with context-specific behavioral equivalence of PobSAM components. PobSAM is a flexible formal model for developing and modeling evolving self-adaptive systems. A PobSAM model is a collection of actors, views, and autonomous managers. Autonomous managers govern the behavior of actors by enforcing suitable context-based policies. Views provide contextual information for managers to control and adapt the actors behavior. Managers are the core components used to realize adaptation by changing their policies. They are modeled as meta-actors whose configurations are described using a multi-sorted algebra called CA. The behavior of mangers depends on the context in which they are executing. In this paper, we present an equational theory to reason about context-specific behavioral equivalence of managers independently from actors. To this end, we introduce and axiomatize a new operator to consider the interaction of managers and the context. This equational theory is based on the notion of statebased bisimilarity and allows us to reason about the behavioral equivalence of managers as well as the behavioral equivalence of the constitutes of managers (i.e., policies and configurations). We illustrate our approach through an example.