Self-Similarity Breeds Resilience

Self-similarity is the property of a system being similar to a part of itself. We posit that a special class of behaviourally self-similar systems exhibits a degree of resilience to adversarial behaviour. We formalise the notions of system, adversary and resilience in operational terms, based on transition systems and observations. While the general problem of proving systems to be behaviourally selfsimilar is undecidable, we show, by casting them in the framework of well-structured transition systems, that there is an interesting class of systems for which the problem is decidable. We illustrate our prescriptive framework for resilience with some small examples, e.g., systems robust to failures in a fail-stop model, and those avoiding side-channel attacks.