Symmetric and efficient synthesis

Since the formulation of the synthesis problem for reactive systems by Church in the 60s, research on synthesis has lead to both theoretical insights and practical approaches for automatically constructing systems from their specifications. While the first solution of the problem was given by Büchi as early as 1969, only very recently, focus has shifted towards identifying ways to exploit the structure in reactive system specifications in order to lift the scalability of synthesis to industrial-sized designs. The recent progress in synthesis not only lead to a renewed interest in the subject, but also shed light onto the downsides of current synthesis approaches. In the original formulation of the problem, the structure of the produced solutions was not a concern. Experiments with current synthesis approaches has however shown that the computed implementations are usually very hard to understand and have little of the structure that manually constructed implementations have. Furthermore, the scalability of current synthesis approaches is still deemed to be insufficient for many industrial application scenarios, which prevents the introduction of reactive synthesis technology into industrial design flows. In this thesis, we tackle both of these problems for reactive synthesis. To counter the insufficient structure in the solutions, we analyse the problem of symmetric synthesis. In this alternative synthesis problem, the aim is to compute a solution that consists of multiple copies of the same process such that the overall system satisfies the specification. Such systems have no centralised control units, and are considered to be more robust and easier to maintain. We characterise undecidable and decidable cases of the problem, and provide a synthesis algorithm for rotation-symmetric architectures, which capture many cases of practical relevance. To improve the scalability in synthesis, we start with a simple but scalable approach to reactive synthesis that has shown its principal applicability in the field, and extend its main idea both in terms of scope and usability. We enhance its expressivity in a way that allows to synthesise robust systems, and remove its limitation to specifications of a very special form. Both improvements yield theoretical insights into the synthesis problem: we characterise which specification classes can be supported in synthesis approaches that use parity games with a fixed number of colours as the underlying computation model, and examine the properties of universal very-weak automata, on which we base a synthesis workflow that combines ease of specification with a low complexity of the underlying game solving step. As a side-result, we also obtain the first procedure to translate a formula in linear-time temporal logic (LTL) to a computation tree logic (CTL) formula with only universal path quantifiers, whenever possible. The new results on symmetric and efficient reactive synthesis are complemented by an easily accessible introductory chapter to the field of reactive synthesis that can also be read in isolation.paddle apparatus with membrane holder were identified.Trotz der Vorzüge der Synthese reaktiver Systeme gegenüber der manuellen Konstruktion solcher Systeme ist Synthese noch nicht als Teil industrieller Vorgehensmodelle etabliert. Als Hauptgrund für diese Diskrepanz gilt allgemein, dass sowohl die Qualität der synthetisierten Systeme bei Anwendung bisheriger Methoden unzureichend ist, als auch die Skalierbarkeit aktueller Syntheseverfahren der Verbesserung bedarf. Diese Dissertation behandelt beide diese Probleme der Synthese reaktiver Systeme auf breiter Front. Zur Verbesserung der Qualität synthetisierter Systeme wird die Synthese von strukturierten Systemen betrachtet. Experimente mit aktuellen Syntheseverfahren haben gezeigt, dass die erzeugten Implementierungen oft schwer zu verstehen sind und anders als handgeschriebene Implementierungen kaum Struktur haben. Abhilfe verschafft die Beschränkung auf die Erzeugung symmetrischer Systeme, die aus mehreren Kopien des selben Prozesses bestehen, so dass das Gesamtsystem die Spezifikation erfüllt. Solche Systeme haben keine zentrale Koordinationskomponente und werden allgemein als robuster und einfacher zu warten eingestuft. In dieser Dissertation werden entscheidbare und unentscheidbare Fälle des symmetrischen Syntheseproblems identifiziert und ein Synthesealgorithmus für rotationssymmetrische Systeme beschrieben. Diese Systemklasse deckt viele praktisch relevante Architekturen ab. Um das Problem der mangelnden Skalierbarkeit anzugehen, wird die Hauptidee des Generalised Reactivity(1) Syntheseansatzes, welcher seine praktische Anwendbarkeit bereits unter Beweis gestellt hat, aufgegriffen und sowohl bezüglich der Expressivität als auch der Benutzbarkeit vervollständigt. Die Erweiterung der Expressivität ermöglicht es, den resultierenden Ansatz für die Synthese robuster Systeme zu nutzen, während die Benutzbarkeit für industrielle Anwendungen durch die Aufhebung der Beschränkung, dass die Spezifikation eine sehr spezielle Form haben muss, erreicht wird. Beide Erweiterungen geben Einsicht in die Theorie der Synthese: Zum einen wird die Klasse der Spezifikationen, die in Syntheseansätzen verwendet werden können, die auf dem Lösen von Paritätsspielen mit einer vordefinierten Anzahl von Farben basieren, charakterisiert. Zum anderen wird Einsicht in die Eigenschaften universeller sehr schwacher Automaten gegeben. Ein Nebenprodukt der neuen Syntheseverfahren ist die erste Prozedur, um einen Ausdruck in linear-time temporal logic (LTL) in computation tree logic mit universellen Pfadquantoren (ACTL) zu übersetzen, wann immer dies möglich ist. Die Resultate zur symmetrischen und effizienten reaktiven Synthese werden von einer didaktisch aufbereiteten Einführung in das Gebiet der reaktiven Synthese begleitet, welche auch unabhängig von den übrigen Teilen der Dissertation gelesen werden kann

Using Ontologies in Autonomous Robots Engineering

The construction and operation of autonomous robots is heavily based of systemic conceptualizations of the reality constituted by the robot, its controller and the environment where it performs. In this chapter we address the role that computer ontologies play in the whole life cycle—engineering and operation—of autonomous robots: from its conception and construction by human engineering teams to deployment and autonomous operation in dynamic and uncertain environments. This chapter summarizes the state of the art, gives some examples and establishes a roadmap for future activity in this domain to produce shareable ontologies that could streamline autonomous robot development and exploitation

Model and Proof Theory of Constructive ALC, Constructive Description Logics

Description logics (DLs) represent a widely studied logical formalism with a significant impact in the field of knowledge representation and the Semantic Web. However, they are equipped with a classical descriptive semantics that is characterised by a platonic notion of truth, being insufficiently expressive to deal with evolving and incomplete information, as from data streams or ongoing processes. Such partially determined and incomplete knowledge can be expressed by relying on a constructive semantics. This thesis investigates the model and proof theory of a constructive variant of the basic description logic ALC, called cALC. The semantic dimension of constructive DLs is investigated by replacing the classical binary truth interpretation of ALC with a constructive notion of truth. This semantic characterisation is crucial to represent applications with partial information adequately, and to achieve both consistency under abstraction as well as robustness under refinement, and on the other hand is compatible with the Curry-Howard isomorphism in order to form the cornerstone for a DL-based type theory. The proof theory of cALC is investigated by giving a sound and complete Hilbert-style axiomatisation, a Gentzen-style sequent calculus and a labelled tableau calculus showing finite model property and decidability. Moreover, cALC can be strengthened towards normal intuitionistic modal logics and classical ALC in terms of sound and complete extensions and hereby forms a starting point for the systematic investigation of a constructive correspondence theory.Beschreibungslogiken (BLen) stellen einen vieluntersuchten logischen Formalismus dar, der den Bereich der Wissensrepräsentation und das Semantic Web signifikant geprägt hat. Allerdings basieren BLen meist auf einer klassischen deskriptiven Semantik, die gekennzeichnet ist durch einen idealisierten Wahrheitsbegriff nach Platons Ideenlehre, weshalb diese unzureichend ausdrucksstark sind, um in Entwicklung befindliches und unvollständiges Wissen zu repräsentieren, wie es beispielsweise durch Datenströme oder fortlaufende Prozesse generiert wird. Derartiges partiell festgelegtes und unvollständiges Wissen lässt sich auf der Basis einer konstruktiven Semantik ausdrücken. Diese Arbeit untersucht die Model- und Beweistheorie einer konstruktiven Variante der Basis-BL ALC, die im Folgenden als cALC bezeichnet wird. Die Semantik dieser konstruktiven Beschreibungslogik resultiert daraus, die traditionelle zweiwertige Interpretation logischer Aussagen des Systems ALC durch einen konstruktiven Wahrheitsbegriff zu ersetzen. Eine derartige Interpretation ist die Voraussetzung dafür, um einerseits Anwendungen mit partiellem Wissen angemessen zu repräsentieren, und sowohl die Konsistenz logischer Aussagen unter Abstraktion als auch ihre Robustheit unter Verfeinerung zu gewährleisten, und andererseits um den Grundstein für eine Beschreibungslogik-basierte Typentheorie gemäß dem Curry-Howard Isomorphismus zu legen. Die Ergebnisse der Untersuchung der Beweistheorie von cALC umfassen eine vollständige und korrekte Hilbert Axiomatisierung, einen Gentzen Sequenzenkalkül, und ein semantisches Tableaukalkül, sowie Beweise zur endlichen Modelleigenschaft und Entscheidbarkeit. Darüber hinaus kann cALC zu normaler intuitionistischer Modallogik und klassischem ALC durch vollständige und korrekte Erweiterungen ausgebaut werden, und bildet damit einen Startpunkt für die systematische Untersuchung einer konstruktiven Korrespondenztheorie

A Design-by-Contract based Approach for Architectural Modelling and Analysis

Research on software architectures has been active since the early nineties, leading to a number of different architecture description languages (ADL). Given their importance in facilitating the communication of crucial system properties to different stakeholders and their analysis early on in the development of a system this is understandable. However, practitioners rarely use ADLs, and, instead, they insist on using the Unified Modelling Language (UML) for specifying software architectures. I attribute this to three main issues that have not been addressed altogether by the existing ADLs. Firstly, in their attempt to support formal analysis, current ADLs employ formal notations (i.e., mostly process algebras) that are rarely used among practitioners. Secondly, many ADLs focus on components in specifying software architectures, neglecting the first-class specification of complex interaction protocols as connectors. They view connectors as simple interaction links that merely identify the communicating components and their basic communication style (e.g., procedure call). So, complex interaction protocols are specified as part of components, which however reduce the re-usability of both. Lastly, there are also some ADLs that do support complex connectors. However, these include a centralised glue element in their connector structure that imposes a global ordering of actions on the interacting components. Such global constraints are not always realisable in a decentralised manner by the components that participate in these protocols. In this PhD thesis, I introduce a new architecture description language called XCD that supports the formal specification of software architectures without employing a complex formal notation and offers first-class connectors for maximising the re-use of components and protocols. Furthermore, by omitting any units for specifying global constraints (i.e., glue), the architecture specifications in XCD are guaranteed to be realisable in a decentralised manner. I show in the thesis how XCD extends Design-by-Contract (DbC) for specifying (i) protocol-independent components and (ii) complex connectors, which can impose only local constraints to guarantee their realisability. Use of DbC will hopefully make it easier for practitioners to use the language, compared to languages using process algebras. I also show the precise translation of XCD into SPIN’s formal ProMeLa language for formally verifying software architectures that (i) services offered by components are always used correctly, (ii) the component behaviours are always complete, (iii)there are no race-conditions, (iv) there is no deadlock, and (v) for components having event communications, there is no overflow of event buffers. Finally, I evaluate XCD via five well-known case studies and illustrate XCD’s enhanced modularity, expressive DbC-based notation, and guaranteed realisability for architecture specifications

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Semantics and the stratification of explanation in cognitive science

This work is concerned with a pervasive problem in Cognitive Science which I have called the "stratificational" approach. I argue that the division into "levels of explanation" that runs as a constant theme through much work in Cognitive Science and in particular natural language semantics, is in direct conflict with neuroscientific evidence. I claim it is also in conflict with a right understanding of the philosophical notion of "evidence". The neuroscientific work is linked with the philosophical problem to provide a critique of concrete cases of research within the natural language semantics community. More recent neuroscientifically aware research is examined and it is demonstrated that it suffers similar problems due to the same deep running assumptions as those which effect traditional formalist theory. The contribution of this thesis is thought to be that of a demonstration of the essential nature and indeed the ubiquity of the basic assumptions in the field. Also, a new link is forged between the concerns of the formalists and certain seemingly more abstract philosophical work. This link enables us to see how much philosophical problems infect research into cognition and language. It is argued that practical research in Cognitive Science simply cannot be seen to be independent of the philosophical basis of the entire subject. The resulting picture of Cognitive Science and its place is outlined and explored with special emphasis on what I have called the "Principle of Semantic Indistinguishabliity" which says that the contribution of what can be broadly termed "environment" is epitemologically opaque to our cognition. The importance of this principle is discussed.The purpose of this work is to draw out a fundamental thread of reasoning and methodology that underlies most traditional work, and some not so traditional work, in Cognitive Science. It will be argued that this line of reasoning is at odds with the implications of modern neuroscience and cannot base a reasonable claim to "explain" human cognition. The picture I shall identify is that which I shall call "stratified". This, in general, is an attempt at explanation that divides into "levels of explanation", each with its own concepts that are said to be essential to the explanation of a phenomenon. There are specific and pragmatic manifestations of this, I discuss these in Chapter 3 and 7 in particular. There are also more abstract expressions of the same tendency which I examine mainly in Chapter 6. One of the principle tasks is to demonstrate the links between the assumptions of the more abstract formulations of this approach and th eir pragmatic instantiations in work in Cognitive Science. This allows it to be made clear that certain methodological problems are ubiquitous within the field and are not simply a result of the particular pragmatics of a particular research area.In Cognitive Science as a whole, it is generally appreciated today that there are problems to do with integration of traditional formal systems and the evolutionary and biological aspects of human cognition. One aim of this work is exactly to give an argument, supported from work in the brain sciences, that a certain methodology - particularly that enshrined within formal systems in language semantics - is strongly denied its evidential basis as a result of certain empirical considerations. It is also denied much of its basis as a result of the incongruity between the original motivations of logical formalism and the use to which this formalism is put today. The conclusion of this is that Cognitive Science's role in certain areas is severely limited and it crucially relies on an amount of empirical brain research in places thought usually to be completely separate from the "low-level" evidence from neuroscience. Part of my thesis is that stratified systems and particularly systems of formal logic within linguistics and semantics, cannot possibly be independent in the way imagined. There is also exploration of a general point regarding the character of the relation between strata in a stratified theory. There is, I shall argue, an irresolvable tension between the desire to have separate strata which are both independent but related. We shall see this both in concrete terms in the discussion of Fodor and in the abstract in the discussion of McDowell.George Lakoffhas expressed agreement with this particular premise: " ... linguistic results ... indicate that human reason uses some of the same mechanisms involved in perception and ... human reason can be seen as growing out of perceptual and motor mechanisms."1If this is correct, then I think that there are enormous implications for Cognitive Science in its practise of semantics since the mechanisms of motor and perceptual systems impose radical constraints when applied in the area of semantics.Given this, my aim is to demonstrate that certain seemingly theoryindependent areas of research in Cognitive Science such as linguistics and natural language semantics are actually infected with damaging assumptions from certain misguided philosophical positions. The idea that we can simply model things in Cognitive Science and wait for someone else to sort out the theoretical structure into which all of the models will fit is not tenable. I shall demonstrate this in several concrete cases and couple this with a critique from neuroscience which is crucially related to a more philosophical critique of fundamental assumptions. The structure of the work is as follows. Firstly, I give an overview of foundational issues in Cognitive Science by discussing central works. Then, I introduce the main problems in concrete form by way of an examination of certain approaches to inference in formal semantics. Chapter 4 expands on this in an analysis of the notion of "compositionality" with reference to the "stratificational" approach I find apparent in traditional work in Cognitive Science and the assumptions it disguises. Chapter 5 introduces the themes from neuroscience and the relations they have to the philosophical critique in Chapter 6. In Chapter 7, I demonstrate that the assumptions I have identified are present even in work motivated by a desire to leave behind the formalist program. I explain why this is the case and the implications this has for a correct view of "evidence" in Cognitive Science. At this point, I deal with pertinent objections to my view stemming from the parts of the discipline I have mentioned. Chapter 8 condenses the problem and shows the fundamentals of the whole problem in relief, suggesting what all of the preceding means for Cognitive Science

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.