For years, formal methods have been successfully applied in the railway domain to formally demonstrate safety of railway systems. Despite that, little has been done in the field of formal methods to address the cyber-physical nature of modern railway signalling systems. In this article, we present an approach for a formal development of cyber-physical railway signalling systems that is based on a refinement-based modelling and proof-based verification. Our approach utilises the Event-B formal specification language together with a hybrid system and communication modelling patterns to developing a generic hybrid railway signalling system model that can be further refined to capture a specific railway signalling system. The main technical contribution of this article is the refinement of the hybrid train Event-B model with other railway signalling sub-systems. The complete model of the cyber-physical railway signalling system was formally proved to ensure a safe rolling stock separation and prevent their derailment. Furthermore, the article demonstrates the advantage of the refinement-based development approach of cyber-physical systems, which enables a problem decomposition and in turn reduction in the verification and modelling effort.
Model checking techniques have often been applied to the verification of railway interlocking systems, responsible for guiding trains safely through a given railway network. However, these techniques fail to scale to the interlocking systems controlling large stations, composed of hundreds and even thousands of controlled entities, due to the state space explosion problem. Indeed, interlocking systems exhibit a certain degree of locality that allows some reasoning only on the mere set of entities that regard the train movements, but safe routing through a complex station layout requires a global reservation policy, which can require global state conditions to be taken into account.
In this article, we present a compositional approach aimed at chopping the verification of a large interlocking system into that of smaller fragments, exploiting in each fragment a proper abstraction of the global information on routing state. A proof is given of the thesis that verifying the safety of the smaller fragments is sufficient to verify the safety of the whole network. Experiments using this compositional approach have shown important gains in performance of the verification, as well as in the size of affordable station layouts.
Benzoxazinoids are specialized metabolites that modulate plant physiology and plant interactions with their environment. In this review, we synthesize their multiple functions and ecological relevance. We first provide an overview of benzoxazinoid biosynthesis and highlight known regulatory elements involved in modulating their production. We then outline the role of benzoxazinoids in plant nutrition, vegetative and reproductive growth, and defense. We further summarize benzoxazinoid response to environmental factors such as temperature, drought, CO2, light, or nutrient levels and emphasize their potential role in tolerating abiotic stresses. Finally, we argue that benzoxazinoids act as a strong selective force on different trophic levels by shaping the plant interactions with microbes, insect herbivores, and competitor plants. Understanding the pivotal role of benzoxazinoids in plant biology is crucial to apprehend their impact on (agro)ecosystem functioning and diversity.