Type-Theoretic Constructions of the Final Coalgebra of the Finite Powerset Functor

The finite powerset functor is a construct frequently employed for the specification of nondeterministic transition systems as coalgebras. The final coalgebra of the finite powerset functor, whose elements characterize the dynamical behavior of transition systems, is a well-understood object which enjoys many equivalent presentations in set-theoretic foundations based on classical logic. In this paper, we discuss various constructions of the final coalgebra of the finite powerset functor in constructive type theory, and we formalize our results in the Cubical Agda proof assistant. Using setoids, the final coalgebra of the finite powerset functor can be defined from the final coalgebra of the list functor. Using types instead of setoids, as it is common in homotopy type theory, one can specify the finite powerset datatype as a higher inductive type and define its final coalgebra as a coinductive type. Another construction is obtained by quotienting the final coalgebra of the list functor, but the proof of finality requires the assumption of the axiom of choice. We conclude the paper with an analysis of a classical construction by James Worrell, and show that its adaptation to our constructive setting requires the presence of classical axioms such as countable choice and the lesser limited principle of omniscience

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

CLASS: A Logical Foundation for Typeful Programming with Shared State

Software construction depends on imperative state sharing and concurrency, which are naturally present in several application domains and are also exploited to improve the structure and efficiency of computer programs. However, reasoning about concurrency and shared mutable state is hard, error-prone and the source of many programming bugs, such as memory leaks, data corruption, deadlocks and non-termination. In this thesis, we develop CLASS: a core session-based language with a lightweight substructural type system, that results from a principled extension of the propositions-astypes correspondence with second-order classical linear logic. More concretely, CLASS offers support for session-based communication, mutex-protected first-class reference cells, dynamic state sharing, generic polymorphic algorithms, data abstraction and primitive recursion. CLASS expresses and types significant realistic programs, that manipulate memoryefficient linked data structures (linked lists, binary search trees) with support for updates in-place, shareable concurrent ADTs (counters, stacks, functional and imperative queues), resource synchronisation methods (fork-joins, barriers, dining philosophers, generic corecursive protocols). All of these examples are guaranteed to be safe, a result that follows by the logical approach. The linear logical foundations guarantee that well-typed CLASS programs do not go wrong: they never deadlock on communication or reference cell acquisition, do not leak memory and always terminate, even if they share complex data structures protected by synchronisation primitives. Furthermore, since we follow a propositions-as-types approach, we can reason about the behaviour of concurrent stateful processes by algebraic program manipulation. The feasibility of our approach is witnessed by the implementation of a type checker and interpreter for CLASS, which validates and guides the development of many realistic programs. The implementation is available with an open-source license, together with several examples.A construção de software depende de estado partilhado imperativo e concorrência, que estão naturalmente presentes em vários domínios de aplicação e que também são explorados para melhorar o a estrutura e o desempenho dos programas. No entanto, raciocinar sobre concorrência e estado mutável partilhado é difícil e propenso à introdução de erros e muitos bugs de programação, tais como fugas de memória, corrupção de dados, programas bloqueados e programas que não terminam a sua execução. Nesta tese, desenvolvemos CLASS: uma linguagem baseada em sessões, com um sistema de tipos leve e subestrutural, que resulta de uma extensão metodológica da correspondência proposições-como-tipos com a lógica linear clássica de segunda ordem. Mais concretamente, a linguagem CLASS oferece suporte para comunicação baseada em sessões, células de memória protegidas com mutexes de primeira classe, partilha dinâmica de estado, algoritmos polimórficos genéricos, abstração de dados e recursão primitiva. A linguagem CLASS expressa e tipifica programas realistas significativos, que manipulam estruturas de dados ligadas eficientes (listas ligadas, árvores de pesquisa binária) suportando actualização imperativa local, TDAs partilhados e concorrentes (contadores, pilhas, filas funcionais e imperativas), métodos de sincronização e partilha de recursos (bifurcar-juntar, barreiras, jantar de filósofos, protocolos genéricos corecursivos). Todos estes exemplos são seguros, uma garantia que resulta da nossa abordagem lógica. Os fundamentos, baseados na lógica linear, garantem que programas em CLASS bem tipificados não incorrem em erros: nunca bloqueiam, quer na comunicação, quer na aquisição de células de memória, nunca causam fugas de memória e terminam sempre, mesmo que compartilhem estruturas de dados complexas protegidas por primitivas de sincronização. Além disso, uma vez que seguimos uma abordagem de proposições-comotipos, podemos raciocinar sobre o comportamento de processos concorrentes, que usam estado, através de manipulação algébrica. A viabilidade da nossa abordagem é evidenciada pela implementação de um verificador de tipos e interpretador para a linguagem CLASS, que valida e orienta o desenvolvimento de vários programs realistas. A implementação está disponível com uma licença de acesso livre, juntamente com inúmeros exemplos

A compositional analysis of broadcasting embedded systems

This work takes as its starting point D Kendall's CANdle/bCANdle algebraic framework for formal modelling and specification of broadcasting embedded systems based on CAN networks. Checking real-time properties of such systems is beset by problems of state-space explosion and so a scheme is given for recasting systems specified in Kendall's framework as parallel compositions of timed automata; a CAN network channel is modelled as an automaton. This recasting is shown to be bi-similar to the original bCANdle model. In the recast framework,"compositionality" theorems allow one to infer that a model of a system is simulated by some abstraction of the model, and hence that properties of the model expressible in ACTL can be inferred from analogous properties of the abstraction. These theorems are reminiscent of "assume-guarantee" reasoning allowing one to build simulations component-wise although, unfortunately, components participating in a "broadcast" are required to be abstracted "atomically". Case studies are presented to show how this can be used in practice, and how systems which take impossibly long to model-check can tackled by compositional methods. The work is of broader interest also, as the models are built as UPPAAL systems and the compositionality theorems apply to any UPPAAL system in which the components do not share local variables. The method could for instance extend to systems using some network other than CAN, provided it can be modelled by timed automata. Possibilities also exist for building it into an automated tool, complementing other methods such as counterexample- guided abstraction refinement

Large scale parallel state space search utilizing graphics processing units and solid state disks

The evolution of science is a double-track process composed of theoretical insights on the one hand and practical inventions on the other one. While in most cases new theoretical insights motivate hardware developers to produce systems following the theory, in some cases the shown hardware solutions force theoretical research to forecast the results to expect. Progress in computer science rely on two aspects, processing information and storing it. Improving one side without touching the other will evidently impose new problems without producing a real alternative solution to the problem. While decreasing the time to solve a challenge may provide a solution to long term problems it will fail in solving problems which require much storage. In contrast, increasing the available amount of space for information storage will definitively allow harder problems to be solved by offering enough time. This work studies two recent developments in the hardware to utilize them in the domain of graph searching. The trend to discontinue information storage on magnetic disks and use electronic media instead and the tendency to parallelize the computation to speed up information processing are analyzed. Storing information on rotating magnetic disk has become the standard way since a couple of years and has reached a point where the storage capacity can be seen as infinite due to the possibility of adding new drives instantly with low costs. However, while the possible storage capacity increases every year, the transferring speed does not. At the beginning of this work, solid state media appeared on the market, slowly suppressing hard disks in speed demanding applications. Today, when finishing this work solid state drives are replacing magnetic disks in mobile computing, and computing centers use them as caching media to increase information retrieving speed. The reason is the huge advantage in random access where the speed does not drop so significantly as with magnetic drives. While storing and retrieving huge amounts of information is one side of the medal, the other one is the processing speed. Here the trend from increasing the clock frequency of single processors stagnated in 2006 and the manufacturers started to combine multiple cores in one processor. While a CPU is a general purpose processor the manufacturers of graphics processing units (GPUs) encounter the challenge to perform the same computation for a large number of image points. Here, a parallelization offers huge advantages, so modern graphics cards have evolved to highly parallel computing instances with several hundreds of cores. The challenge is to utilize these processors in other domains than graphics processing. One of the vastly used tasks in computer science is search. Not only disciplines with an obvious search but also in software testing searching a graph is the crucial aspect. Strategies which enable to examine larger graphs, be it by reducing the number of considered nodes or by increasing the searching speed, have to be developed to battle the rising challenges. This work enhances searching in multiple scientific domains like explicit state Model Checking, Action Planning, Game Solving and Probabilistic Model Checking proposing strategies to find solutions for the search problems. Providing an universal search strategy which can be used in all environments to utilize solid state media and graphics processing units is not possible due to the heterogeneous aspects of the domains. Thus, this work presents a tool kit of strategies tied together in an universal three stage strategy. In the first stage the edges leaving a node are determined, in the second stage the algorithm follows the edges to generate nodes. The duplicate detection in stage three compares all newly generated nodes to existing once and avoids multiple expansions. For each stage at least two strategies are proposed and decision hints are given to simplify the selection of the proper strategy. After describing the strategies the kit is evaluated in four domains explaining the choice for the strategy, evaluating its outcome and giving future clues on the topic

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

A compositional analysis of broadcasting embedded systems

This work takes as its starting point D Kendall's CANdle/bCANdle algebraic framework for formal modelling and specification of broadcasting embedded systems based on CAN networks. Checking real-time properties of such systems is beset by problems of state-space explosion and so a scheme is given for recasting systems specified in Kendall's framework as parallel compositions of timed automata; a CAN network channel is modelled as an automaton. This recasting is shown to be bi-similar to the original bCANdle model. In the recast framework,"compositionality" theorems allow one to infer that a model of a system is simulated by some abstraction of the model, and hence that properties of the model expressible in ACTL can be inferred from analogous properties of the abstraction. These theorems are reminiscent of "assume-guarantee" reasoning allowing one to build simulations component-wise although, unfortunately, components participating in a "broadcast" are required to be abstracted "atomically". Case studies are presented to show how this can be used in practice, and how systems which take impossibly long to model-check can tackled by compositional methods. The work is of broader interest also, as the models are built as UPPAAL systems and the compositionality theorems apply to any UPPAAL system in which the components do not share local variables. The method could for instance extend to systems using some network other than CAN, provided it can be modelled by timed automata. Possibilities also exist for building it into an automated tool, complementing other methods such as counterexample- guided abstraction refinement.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A global workspace framework for combined reasoning

Artificial Intelligence research has produced many effective techniques for solving a wide range of problems. Practitioners tend to concentrate their efforts in one particular problem solving paradigm and, in the main, AI research describes new methods for solving particular types of problems or improvements in existing approaches. By contrast, much less research has considered how to fruitfully combine different problem solving techniques. Numerous studies have demonstrated how a combination of reasoning approaches can improve the effectiveness of one of those methods. Others have demonstrated how, by using several different reasoning techniques, a system or method can be developed to accomplish a novel task, that none of the individual techniques could perform. Combined reasoning systems, i.e., systems which apply disparate reasoning techniques in concert, can be more than the sum of their parts. In addition, they gain leverage from advances in the individual methods they encompass. However, the benefits of combined reasoning systems are not easily accessible, and systems have been hand-crafted to very specific tasks in certain domains. This approach means those systems often suffer from a lack of clarity of design and are inflexible to extension. In order for the field of combined reasoning to advance, we need to determine best practice and identify effective general approaches. By developing useful frameworks, we can empower researchers to explore the potential of combined reasoning, and AI in general. We present here a framework for developing combined reasoning systems, based upon Baars’ Global Workspace Theory. The architecture describes a collection of processes, embodying individual reasoning techniques, which communicate via a global workspace. We present, also, a software toolkit which allows users to implement systems according to the framework. We describe how, despite the restrictions of the framework, we have used it to create systems to perform a number of combined reasoning tasks. As well as being as effective as previous implementations, the simplicity of the underlying framework means they are structured in a straightforward and comprehensible manner. It also makes the systems easy to extend to new capabilities, which we demonstrate in a number of case studies. Furthermore, the framework and toolkit we describe allow developers to harness the parallel nature of the underlying theory by enabling them to readily convert their implementations into distributed systems. We have experimented with the framework in a number of application domains and, through these applications, we have contributed to constraint satisfaction problem solving and automated theory formation