21 research outputs found
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