Game-Based Local Model Checking for the Coalgebraic mu-Calculus

The coalgebraic mu-calculus is a generic framework for fixpoint logics with varying branching types that subsumes, besides the standard relational mu-calculus, such diverse logics as the graded mu-calculus, the monotone mu-calculus, the probabilistic mu-calculus, and the alternating-time mu-calculus. In the present work, we give a local model checking algorithm for the coalgebraic mu-calculus using a coalgebraic variant of parity games that runs, under mild assumptions on the complexity of the so-called one-step satisfaction problem, in time p^k where p is a polynomial in the formula and model size and where k is the alternation depth of the formula. We show moreover that under the same assumptions, the model checking problem is in both NP and coNP, improving the complexity in all mentioned non-relational cases. If one-step satisfaction can be solved by means of small finite games, we moreover obtain standard parity games, ensuring quasi-polynomial run time. This applies in particular to the monotone mu-calculus, the alternating-time mu-calculus, and the graded mu-calculus with grades coded in unary

Families of Symmetries as Efficient Models of Resource Binding

AbstractCalculi that feature resource-allocating constructs (e.g. the pi-calculus or the fusion calculus) require special kinds of models. The best-known ones are presheaves and nominal sets. But named sets have the advantage of being finite in a wide range of cases where the other two are infinite. The three models are equivalent. Finiteness of named sets is strictly related to the notion of finite support in nominal sets and the corresponding presheaves. We show that named sets are generalisd by the categorical model of families, that is, free coproduct completions, indexed by symmetries, and explain how locality of interfaces gives good computational properties to families. We generalise previous equivalence results by introducing a notion of minimal support in presheaf categories indexed over small categories of monos. Functors and categories of coalgebras may be defined over families. We show that the final coalgebra has the greatest possible symmetry up-to bisimilarity, which can be computed by iteration along the terminal sequence, thanks to finiteness of the representation

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

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

Coalgebraic Methods for Object-Oriented Specification

This thesis is about coalgebraic methods in software specification and verification. It extends known techniques of coalgebraic specification to a more general level to pave the way for real world applications of software verification. There are two main contributions of the present thesis: 1. Chapter 3 proposes a generalisation of the familiar notion of coalgebra such that classes containing methods with arbitrary types (including binary methods) can be modelled with these generalised coalgebras. 2. Chapter 4 presents the specification language CCSL (short for Coalgebraic Class Specification Language), its syntax, its semantics, and a prototype compiler that translates CCSL into higher-order logic.Die Dissertation beschreibt coalgebraische Mittel und Methoden zur Softwarespezifikation und -verifikation. Die Ergebnisse dieser Dissertation vereinfachen die Anwendung coalgebraischer Spezifikations- und Verifikationstechniken und erweitern deren Anwendbarkeit. Damit werden Softwareverifikation im Allgemeinen und im Besonderen coalgebraische Methoden zur Softwareverifikation der praktischen Anwendbarkeit ein Stück nähergebracht. Diese Dissertation enthält zwei wesentliche Beiträge: 1. Im Kapitel 3 wird eine Erweiterung des klassischen Begriffs der Coalgebra vorgestellt. Diese Erweiterung erlaubt die coalgebraische Modellierung von Klassenschnittstellen mit beliebigen Methodentypen (insbesondere mit binären Methoden). 2. Im Kapitel 4 wird die coalgebraische Spezifikationssprache CCSL (Coalgebraic Class Specification Language) vorgestellt. Die Bescheibung umfasst Syntax, Semantik und einen Prototypcompiler, der CCSL Spezifikationen in Logik höherer Ordnung (passend für die Theorembeweiser PVS und Isabelle/HOL) übersetzt