Adaptability checking in complex systems

Abstract

A hierarchical approach for modelling the adaptability features of complex systems is introduced. It is based on a structural level S, describing the adaptation dynamics of the system, and a behavioural level B accounting for the description of the admissible dynamics of the system. Moreover, a unified system, called S[B]S[B], is defined by coupling S and B. The adaptation semantics is such that the S level imposes structural constraints on the B level, which has to adapt whenever it no longer can satisfy them. In this context, we introduce weak and strong adaptability, i.e. the ability of a system to adapt for some evolution paths or for all possible evolutions, respectively. We provide a relational characterisation for these two notions and we show that adaptability checking, i.e. deciding if a system is weakly or strongly adaptable, can be reduced to a CTL model checking problem. We apply the model and the theoretical results to the case study of a motion controller of autonomous transport vehicles

Topological Characterization of Complex Systems: Using Persistent Entropy

“…Given an equilibrium condition (steady state) characterizing the system, an external or internal factor may alter this equilibrium and make the system react towards a new equilibrium [12]. If the system is observed at a certain moment, as when a sample of the data is taken, it may still satisfy the current equilibrium condition.…”

“…For a more formal definition of the link between the observables and the dynamics of S[B], we refer to [12]. The structural level S of the derived S[B] model can be defined as a persistent entropy automaton (PEA), which is a tuple (R, Λ, ρ 0 , H, − → S , L) where:…”

“…Our contribution has been inspired by S[B] [11], a paradigm for modeling complex systems. It was used as a general framework for modeling adaptivity in software systems [12], but it was conceived for all kinds of complex systems (biological, physical, chemical, and so on). Figure 2 graphically shows our methodology.…”

A Graph Grammar for Modelling RNA Folding

“…In general, self-adaptive systems are able to modify their own behaviour according to their current configuration and the perception of the environment in which they operate. This feature is formalized by the S[B] paradigm [9,8,10]. An S[B] model, following the paradigm, comprises two coupled levels: the behavioural level B, which describes the admissible dynamics of the system and the structural level S, accounting for the invariant features of the system and regulating its entangled behaviour as a whole.…”

“…Since an RNA molecule exhibits an auto-regulative mechanism similar to the adaptability process of complex systems [8], a new way of modelling the prediction of an RNA secondary structure can be investigated. The idea is to model the RNA folding by a graph-based approach that allows to represent the evolution of the structure step by step.…”