A method for rigorous design of reconfigurable systems

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements. In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The first author is further supported by the BPD FCT Grant SFRH/BPD/103004/2014, and R. Neves is sponsored by FCT Grant SFRH/BD/52234/2013. M.A. Martins is also funded by the EU FP7 Marie Curie PIRSESGA-2012-318986 project GeTFun: Generalizing Truth-Functionality

Coalgebra for the working software engineer

Often referred to as ‘the mathematics of dynamical, state-based systems’, Coalgebra claims to provide a compositional and uniform framework to spec ify, analyse and reason about state and behaviour in computing. This paper addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one is interested in properties that are preserved along the system’s evolution, the so-called ‘business rules’ or system’s invariants, as well as in liveness requirements, stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system’s dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand. In this context, the paper revisits Coalgebra from a computational perspective, focussing on three topics central to software design: how systems are modelled, how models are composed, and finally, how properties of their behaviours can be expressed and verified.Fuzziness, as a way to express imprecision, or uncertainty, in computation is an important feature in a number of current application scenarios: from hybrid systems interfacing with sensor networks with error boundaries, to knowledge bases collecting data from often non-coincident human experts. Their abstraction in e.g. fuzzy transition systems led to a number of mathematical structures to model this sort of systems and reason about them. This paper adds two more elements to this family: two modal logics, framed as institutions, to reason about fuzzy transition systems and the corresponding processes. This paves the way to the development, in the second part of the paper, of an associated theory of structured specification for fuzzy computational systems

Graph-based software specification and verification

The (in)correct functioning of many software systems heavily influences how\ud we qualify our daily lives. Software companies as well as academic computer\ud science research groups spend much effort on applying and developing techniques for improving the correctness of software systems. In this dissertation\ud we focus on using and developing graph-based techniques to specify and verify\ud the behaviour of software systems in general, and object-oriented systems more\ud specifically. We elaborate on two ways to improve the correctness (and thereby\ud the quality) of such systems.\ud Firstly, we investigate the potential of using the graph transformation tech-\ud nique to formally specify the dynamic semantics of (object-oriented) program-\ud ming languages. Those semantics are typically specified in natural language.\ud Such specifications are often hard to understand or even ambiguous. We show\ud how the graph transformation framework provides formal and intuitive means\ud for their specification.\ud Secondly, we develop techniques to verify systems of which the behaviour is\ud specified as graph production systems. For the verification of such systems, we\ud introduce an algorithm that combines a well-known on-the-\ud y model checking\ud algorithm with ideas from bounded model checking. One of the main prob-\ud lems of model checking is the state-explosion problem. This problem is often\ud tackled using partial order reduction techniques. Unfortunately, many such\ud techniques are based on assumptions that do not hold for graph production sys-\ud tems. Therefore, we develop a new dynamic partial order reduction algorithm\ud based on selecting so-called probe sets and prove its correctness.\ud Most of the techniques developed in this dissertation have been implemented\ud in the graph transformation tool GROOVE

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Gauge Models of Topological Phases and Applications to Quantum Gravity

In 2+1 dimensions, gravity is an SU(2) topological gauge theory that can be written as BF theory. In the condensed matter literature, the Hamiltonian realization of BF theory for finite groups is known as the Kitaev model. The corresponding Hamiltonian yields magnetic and electric point-like excitations, both supported by punctures. In this context, the cylinder plays a special role since the gluing of two cylinders results in another cylinder, hence defining an algebra on the Hilbert space of states, referred to as Ocneanu's tube algebra. By choosing specific graph-states on the cylinder, we can confirm explicitly that this algebra is equivalent to the Drinfel'd double of the gauge group. The representation theory of the Drinfel'd double can then be used to define a basis of excited states associated with any punctured Riemann surface. This result can be adapted so as to define a new basis for the gauge invariant Hilbert space of lattice gauge theories, and a fortiori loop quantum gravity, replacing the well-known spin network basis. In doing so, we naturally shift the focus from the underlying lattice to the excitations themselves, this notion of excitations being understood with respect to a given vacuum state, namely the so-called BF vacuum. This basis diagonalizes so-called ribbon operators that provide Dirac observables. Furthermore, it has an inherent hierarchical organization allowing to design states with a multi-scale structure. This turns out to be extremely precious for studying the large scale structure of the theory. It also provides a new notion of subsystems for gauge theories. Being solely based on excitations, this leads to a completely relational way of defining regions. This can be used to define a new notion of entanglement entropy for lattice gauge theories and (2+1)d gravity coupled to point particles. These techniques can also be generalized so as to define excitation bases for (3+1)d gauge models of topological phases. Two approaches are considered in this thesis. The first one consists in generalizing Ocneanu's tube algebra by replacing the cylinder with the manifold obtained by cutting open a three-torus along one direction. This defines an algebraic structure extending the Drinfel'd double that can be used in a similar fashion as in (2+1)d. The other approach relies on Heegaard splittings of three-manifolds which perform a decomposition into handle-bodies along so-called Heegaard surfaces. We use this technique to encode the Hilbert space of flat connections with curvature excitations of a three-manifold into the Hilbert space of flat connections on a 2d Heegaard surface, hence making the results derived in (2+1)d available to the study of the (3+1)d case

Efficient abstractions for visualization and interaction

Abstractions, such as functions and methods, are an essential tool for any programmer. Abstractions encapsulate the details of a computation: the programmer only needs to know what the abstraction achieves, not how it achieves it. However, using abstractions can come at a cost: the resulting program may be inefficient. This can lead to programmers not using some abstractions, instead writing the entire functionality from the ground up. In this thesis, we present several results that make this situation less likely when programming interactive visualizations. We present results that make abstractions more efficient in the areas of graphics, layout and events

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

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems