AN INVESTIGATION OF LOWER SECONDARY PUPILS' IMAGES OF MATHEMATICS AND MATHEMATICIANS

This thesis reports on a three-part research project in which the images of mathematics and mathematicians held by lower secondary pupils were investigated. A survey tool which asked pupils to draw a picture of a mathematician at work, and which included a Likert-type scale and open-ended writing prompts, was designed and developed for use in an international study of pupils in five countries (n = 476). The results indicate that while some pupils hold stereotypical images in common, all pupils appear to know very little about mathematicians and the work they do. Mathematicians' invisibility to pupils of this age appears to affect their images of mathematics. The tool was refined and utilised again as part of two interventions in the United States: the first attempted to see if images would be affected by a unit in graph theory and discrete mathematics topics (n = 28); the second brought pupils (n = 174) together with a panel of mathematicians. Each intervention had different strengths, but both widened pupils' views of mathematics, enabling them to see it as more than just a study of numbers. In a third small study, professionals in the mathematics field (n = 106) from ten countries were asked in a short survey to comment on Who is a mathematician? and Who may call oneself one? Findings of this portion of the study indicate a lack of a unified vision among members of the mathematics community and some evidence of an elitism which would restrict who may define themselves as a mathematician

Foundations and techniques for software reconfigurability

Programa de doutoramento em Informática das Universidades do Minho, de Aveiro e do PortoThe qualifier reconfigurable is used for software systems which behave differently in different modes of operation (often called configurations) and commute between them along their lifetime. Such systems, which evolve in response to external or internal stimulus, are everywhere: from e-Health or e-Government integrated services to sensor networks, from domestic appliances to complex systems distributed and collaborating over the web, from safety or mission-critical applications to massive parallel software. There are two basic approaches to formally capture requirements of this sort of systems: one emphasizes behaviour and its evolution; the other focus on data and their transformations. Within the first paradigm, reconfigurable systems are regarded as (some variant of) state-machines whose states correspond to the different configurations they may assume. On the other hand, in data-oriented approaches the system’s functionality is specified in terms of input-output relations modelling operations on data. A specification presents a theory in a suitable logic, expressed over a signature which captures its syntactic interface. Its semantics is a class of concrete algebras or relational structures, acting as models for the specified theory. The observation that whatever services a reconfigurable system may offer, at each moment, may depend on the stage of its evolution, suggests that both dimensions (data and behaviour) are interconnected and should be combined. In particular, each node in the transition system which describes a reconfiguration space, may be endowed with a local structure modelling the functionality of the respective configuration. This is the basic insight of a configurations-as-local-models specification style. These specifications are modeled by structured state-machines, states denoting complex structures, rather than sets. A specification for this sort of system should be able to make assertions both about the transition dynamics and, locally, about each particular configuration. This leads to the adoption of hybrid logic, which adds to the modal description of transition structures the ability to refer to specific states, as the lingua franca for a suitable specification method. On the other hand, specific applications may require specific logics to describe their configurations. For example, requirements expressed equationally lead to a configurations-as-algebras perspective. But depending on their nature one could also naturally end up in configurations-as-relational-structutres, or probabilistic spaces or even in configurations-as-Kripke-structutres, if first-order, fuzzy or modal logic is locally used. The aim of this thesis is to develop the foundations for a specification method based on these principles. To subsume all the possibilities above our approach builds on very general grounds. Therefore, instead of committing to a particular version of hybrid logic, we start by choosing a specific logic for expressing requirements at the configuration (static) level. This is later taken as the base logic on top of which the characteristic features of hybrid logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds), are developed. This process is called hybridisation and is one of the main technical contributions of this thesis. To be completely general, it is framed in the context of the theory of institutions of J. Goguen and R. Burstall, each logic (base and hybridised) being treated abstractly as an institution. In this setting the thesis’ contributions are the following: A method to hybridise arbitrary institutions; this can be understood as a source of logics to support arbitrary configurations-as-local-models specifications. A method to lift encodings (technically, comorphisms) from an institution to a presentation in first-order logic, into encodings from its hybridisation to a presentation in first-order logic; this result paves the way to the introduction of suitable automatised proof support for a wide range of hybridised logics. Suitable characterisations of bisimulation and refinement for models of (generic) hybridisations, which provide canonical, satisfaction preserving relations to identify and relate models. A two-stage specification method for reconfigurable systems based on a global transition structure to capture the system’s reconfiguration space, and a local specification of configurations in whatever logic is found expressive enough for the requirements at hands. A set of additional technics to assist the process of specifying and verifying requirements for reconfigurable systems, with partial tool support.O termo reconfigurável é usado para sistemas de software que se comportam de forma diferente em diferentes modos de operação (frequentemente chamados de configurações) comutando entre eles, ao longo do seu ciclo de vida. Estes sistemas, que evoluem em resposta a estímulos externos e internos, estão por toda a parte, desde sistemas de e-Health ou sistemas integrados de e-Governement, às redes de sensores, das aplicações domésticas aos complexos sistemas distribuidos, dos sistemas críticos de missão ao software de computação paralela. Existem duas abordagens formais para captar requisitos deste tipo de sistemas: uma focada no comportamento e evolução; e outra focada nos dados e respectivas transformações. Segundo o primeiro paradigma, os sistemas reconfiguráveis são abordados por (alguma variante) de máquinas-de-estados, correspondendo, cada um dos seus estados, a uma configuração que o sistema possa assumir. A outra abordagem, orientada aos dados, especifica as funcionalidades do sistema em função de relações de input-output, que modelam operações nos dados. Uma especificação apresenta uma teoria numa lógica adequada, expressa sobre uma assinatura que capta a sua interface sintática. A sua semântica consiste na classe de álgebras, ou estruturas de primeira ordem, que modelam a teoria especificada. A observação de que, a cada momento, os serviços oferecidos por um sistema reconfigurável possam depender do estado da sua evolução, sugere-nos que ambas as dimensões (dados e comportamento) estejam interligados e devam ser combinados. Em particular, cada nó do sistema de transição, que descreve o espaço de reconfigurabilidade, pode ser dotado de uma estrutura local onde as funcionalidades do sistema, na respectiva configuração, são modeladas. Esta é a ideia base da especificação configurações-como-modeloslocais. Tecnicamente, as especificações são modeladas por máquinas de estados estruturadas, onde cada estado denota uma estrutura complexa, ao invés de um conjunto. Uma especificação para este tipo de sistemas deve ser adequada à expressão de asserções acerca da dinâmica de transições, assim como, ao nível local de cada configuração particular. Isto leva-nos à adopção de lógica híbrida, que adiciona, mecanismos para referir estados específicos à expressividade modal dos sistemas de transição, como lingua franca para um método adequado de especificação. Por outro lado, aplicações podem requerer lógicas específicas para descrever as suas configurações. Por exemplo, requisitos expressos por equações devem ser modelados numa perspectiva configurações-como-álgebras. Dependendo da sua natureza, podemos considerar configurações-como-estruturas de primeira ordem, ou configurações-como-espaços probabilísticos ou mesmo configurações-como-estruturas de Kripke quando usadas, localmente, lógica de primeira ordem, lógica fuzzy, ou lógica modal respectivamente. O objectivo da tese é desenvolver os fundamentos para um método de especificação baseado nestes princípios. Por forma a acomodar todas estas possibilidades, a abordagem é desenvolvida sob fundamentos muito genéricos. Ao invés de comprometer a abordagem com uma lógica híbrida particular, partimos da escolha da lógica específica para especificar requisitos ao nível (estáctico) local. Esta lógica é então tomada como lógica de base, sobre a qual os mecanismos da lógica híbrida, tanto ao nível sintáctico (i.e., modalidades, nominais, etc.) como ao semântico (i.e., mundos possíveis), são desenvolvidos. Este processo, que chamamos de hibridização, é uma das principais contribuições técnicas da tese. A generalidade do método resulta do seu desenvolvimento no contexto da teoria das instituições de J. Goguen e R. Burstall. As peincipais contribuições da tese são: • um método para hibridizar instituições arbitrárias; o que pode ser entendido como uma fonte de lógicas para suportar especificações configurações- como-modelos-locais arbitrárias • um método para transportar codificações de uma instituição nas apresentações de primeira ordem (tecnicamente comorfismos), em codificações da sua hibridização em apresentações em primeira ordem; este resultado abre o caminho para a introdução do suporte de prova automático para uma ampla classe de lógicas híbridas; • caracterização de relações de bissimulação e de refinamento para modelos de hibridizações genéricas. Isto oferece relações canónicas, que preservam satisfação, para identificar e relacionar modelos; • um método de especificação para sistemas reconfiguráveis com dois estágios, baseado numa estrutura de transição global, onde o espaço de reconfigurações do sistema é modelado; e numa especificação local das configurações expressa numa lógica escolhida como adequada, aos requisitos a tratar; • um conjunto de técnicas adicionais para assistir o processo de especificação e de verificação de requisitos de sistemas reconfiguráveis com suporte parcial de ferramentas.Fundação para a Ciência e Tecnologia (FCT) and Critical Software S.A., under BDE grant under the contract SFRH/BDE/33650/2009 and by the MONDRIAN Project (FCT) under the contract PTDC/EIA-CCO/108302/2008

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp

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.

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition

NOTIFICATION !!!

All the content of this special edition is retrieved from the conference proceedings published by the European Scientific Institute, ESI. http://eujournal.org/index.php/esj/pages/view/books The European Scientific Journal, ESJ, after approval from the publisher re publishes the papers in a Special edition