Lost in translation: Hybrid-time flows vs. real-time transitions

Recently, hybrid-time flow systems have been introduced as an extension to timed transition systems, hybrid automata, continuous time evolutions of differential equations etc. Furthermore, a number of notions of bisimulation have been defined on these flow systems reflecting abstraction from certain timing properties. In this paper, we research the difference in abstraction level between this new semantic model of flow systems, and the more traditional model of real-time transition systems. We explore translations between the old and new semantic models, and we give a necessary and sufficient condition, called finite-set refutability, for these translations to be without loss of information. Finally, we show that differential inclusions with an upper-semicontinuous, closed and convex right-hand side, are finite-set refutable, and easily extend this result to impuls differential inclusions and hybrid automata

A Formal Methodology for Engineering Heterogeneous Railway Signalling Systems

Ph. D. Thesis.Over the last few decades, the safety assurance of cyber-physical systems has become one of the biggest challenges in the field of model-based system engineering. The challenge arises from an immense complexity of cyber-physical systems which have deeply intertwined physical, software and network system aspects. With significant improvements in a wireless communication and microprocessor technologies, the railway domain has become one of the frontiers for deploying cyber-physical signalling systems. However, because of the safety-critical nature of railway signalling systems, the highest level of safety assurance is essential. This study attempts to address the challenge of guaranteeing the safety of cyber-physical railway signalling systems by proposing a development methodology based on formal methods. In particular, this study is concerned with the safety assurance of heterogeneous cyber-physical railway signalling systems, which have emerged by gradually replacing outdated signalling systems and integrating mainline with urban signalling systems. The main contribution of this work is a formal development methodology of railway signalling systems. The methodology is based on the Event-B modelling language, which provides an expressive modelling language, a stepwise model development and a proof-based model verification. At the core of the methodology is a generic communication-based railway signalling Event-B model, which can be further refined to capture specific heterogeneous or homogeneous railway signalling configurations. In order to make signalling modelling more systematic we developed communication and hybrid railway signalling modelling patterns. The proposed methodology and modelling patterns have been evaluated on two case studies. The evaluation shows that the methodology does provide a system-level railway signalling modelling and verification method. This is crucial for verifying the safety of cyber-physical systems, as safety is dependent on interactions between different subsystems. However, the study has also shown that automatic formal verification of hybrid systems is still a major challenge and must be addressed in the future work in order to make this methodology more practical.(EPSRC and Siemens Rail Automation

Hybrid programs

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and PortoThis thesis studies hybrid systems, an emerging family of devices that combine in their models digital computations and physical processes. They are very quickly becoming a main concern in software engineering, which is explained by the need to develop software products that closely interact with physical attributes of their environment e. g. velocity, time, energy, temperature – typical examples range from micro-sensors and pacemakers, to autonomous vehicles, transport infrastructures and district-wide electric grids. But even if already widespread, these systems entail different combinations of programs with physical processes, and this renders their development a challenging task, still largely unmet by the current programming practices. Our goal is to address this challenge at its core; we wish to isolate the basic interactions between discrete computations and physical processes, and bring forth the programming paradigm that naturally underlies them. In order to do so in a precise and clean way, we resort to monad theory, a well established categorical framework for developing program semantics systematically. We prove the existence of a monad that naturally encodes the aforementioned interactions, and use it to develop and examine the foundations of the paradigm alluded above, which we call hybrid programming: we show how to build, in a methodical way, different programming languages that accommodate amplifiers, differential equations, and discrete assignments – the basic ingredients of hybrid systems – we list all program operations available in the paradigm, introduce if-then-else constructs, abort operations, and different types of feedback. Hybrid systems bring several important aspects of control theory into computer science. One of them is the notion of stability, which refers to a system’s capacity of avoiding significant changes in its output if small variations in its state or input occur. We introduce a notion of stability to hybrid programming, explore it, and show how to analyse hybrid programs with respect to it in a compositional manner. We also introduce hybrid programs with internal memory and show that they form the basis of a component-based software development discipline in hybrid programming. We develop their coalgebraic theory, namely languages, notions of behaviour, and bisimulation. In the process, we introduce new theoretical results on Coalgebra, including improvements of well-known results and proofs on the existence of suitable notions of behaviour for non-deterministic transition systems with infinite state spaces.Esta tese estuda sistemas híbridos, uma família emergente de dispositivos que envolvem diferentes interações entre computações digitais e processos físicos. Estes sistemas estão rapidamente a tornar-se elementos-chave da engenharia de software, o que é explicado pela necessidade de desenvolver produtos que interagem com os atributos físicos do seu ambiente e. g. velocidade, tempo, energia, e temperatura – exemplos típicos variam de micro-sensores e pacemakers, a veículos autónomos, infra-estruturas de transporte, e redes eléctricas distritais. Mas ainda que amplamente usados, estes sistemas são geralmente desenvolvidos de forma pouco sistemática nas prácticas de programação atuais. O objetivo deste trabalho é isolar as interações básicas entre computações digitais e processos físicos, e subsequentemente desenvolver o paradigma de programação subjacente. Para fazer isto de forma precisa, a nossa base de trabalho irá ser a teoria das mónadas, uma estrutura categórica para o desenvolvimento sistemático de semânticas na programação. A partir desta base, provamos a existência de uma mónada que capta as interações acima mencionadas, e usamo-la para desenvolver e examinar os fundamentos do paradigma de programação correspondente a que chamamos programação híbrida: mostramos como construir, de maneira metódica, diferentes linguagens de programação que acomodam amplificadores, equações diferenciais, e atribuições - os ingredientes básicos dos sistemas híbridos - caracterizamos todas as operações sobre programas disponíveis, introduzimos construções if-then-else, operações para lidar com excepções, e diferentes tipos de feedback. Os sistemas híbridos trazem vários aspectos da teoria de controlo para a ciência da computação. Um destes é a noção de estabilidade, que se refere à capacidade de um sistema de evitar mudanças drásticas no seu output se pequenas variações no seu estado ou input ocorrerem. Neste trabalho, desenvolvemos uma noção composicional de estabilidade para a programação híbrida. Introduzimos também programas híbridos com memória interna, que formam a base de uma disciplina de desenvolvimento de software baseado em componentes. Desenvolvemos a sua teoria coalgébrica, nomeadamente linguagens, noções de comportamento e bisimulação. Neste processo, introduzimos também novos resultados teóricos sobre Coalgebra, incluindo melhorias a resultados conhecidos e provas acerca da existência de noções de comportamento para sistemas de transição não determinísiticos com espaço de estados infinitos.The present work was financed by FCT – Fundação para a Ciência e a Tecnologia – with the grant SFRH/BD/52234/2013. Additional support was provided by the PTFLAD Chair on Smart Cities & Smart Governance and by project Dalí (POCI-01-0145-FEDER-016692), the latter funder by ERDF – European Regional Development Fund – through COMPETE 2020 – Operational Programme for Competitiveness and Internationalisation – together with FCT

On Hybrid Systems and the Modal µ-Calculus

. We start from a basic and fruitful idea in current work on the formal analysis and verification of hybrid and real-time systems: the uniform representation of both sorts of state dynamics -- both continuous evolution within a control mode, and the effect of discrete jumps between control modes -- as abstract transition relations over a hybrid space X ` Q \Theta R n , where Q is a finite set of control modes. The resulting "machine" or transition system model is currently analyzed using the resources of concurrent and reactive systems theory and temporal logic verification, abstracted from their original setting of finite state spaces and purely discrete transitions. One such resource is the propositional -calculus: a richly expressive formal logic of transition system models (of arbitrary cardinality), which subsumes virtually all temporal and modal logics. The key move here is to view the transition system models of hybrid automata not merely as some form of "discrete..

On Hybrid Systems and the Modal µ-Calculus (Extended Abstract)

this paper appears in P. Antsaklis et al. (eds.), Hybrid Systems V, LNCS 1567. Springer-Verlag, Berlin, 1999. 38--69