Thesis (M.S.)--Boise State University, 2009. / Includes abstract. Includes bibliographical references (leaves 52-53).

Proof-carrying code is an application of software verification techniques to the problem of ensuring the safety of mobile code. However, previous proof-carrying code systems have assumed that mobile code will faithfully execute the instructions of the program. Realistic implementations of computing systems are susceptible to probabilistic behaviours that can alter the execution of a program in ways that can result in corruption or security breaches. We investigate the use of a probabilistic bytecode language to model deterministic programs that are executed on probabilistic computing systems. To model probabilistic safety properties, a probabilistic logic is adapted to out bytecode instruction language, and soundness is proven. A sketch of a completeness proof of the logic is also shown.

Thesis (M.S.)--Boise State University, 2009. / Title from t.p. of PDF file (viewed June 15, 2010). Includes abstract. Includes bibliographical references (leaves 52-53).

Doctor of Philosophy / Department of Mathematics / Andrew G. Bennett / This dissertation investigates and compares the methods of proof validation utilized by novice and expert mathematicians within the realm of Euclidean geometry. With the use of eye tracking technology, our study presents empirical evidence supporting claims previously studied only through the use of verbal protocols. Our investigation settles a series of contentious results surrounding the practical implementation of the generalized validation strategy called zooming out (Inglis and Alcock, 2012; Weber, Mejia-Ramos, Inglis, and Alcock, 2013). This strategy analyzes the overall structure of a proof as an application of methods or logical chunks. Settling the debate through use of longer and more complicated proofs devoid of blatant errors, we found that validators do not initially skim-read proofs to gain structural insight. We did however confirm the practical implementation of zooming out strategies. The literature identifies within the proof validation process specific differences between novices and experts. We are interested in a holistic understanding of novice and expert validations. We therefore present the direct comparison of entire validation processes that assess the similarity of novice and expert overall validation attempts. We found that the validation processes of novices and experts share a certain degree of similarity. In fact novices tend to be closer to experts than to other novices. And when validations are clustered, the groups are heterogeneous with regard to mathematical maturity. Our investigation expands the proof validation literature by including diagrams in the proof validation process. We found that experts tend to spend more time proportionally on the diagram than novices and that novices spend more time on the text. Furthermore, experts tend to draw more connections within the diagram than novices as indicated by a higher proportion of attentional changes within the diagrams. Experts seem to draw on the power of visualizations within the mathematics itself, spending more time on conceptual understanding and intended connections.

O presente trabalho estuda a aplicação da teoria da distribuição dinâmica do ônus da prova no Direito Processual do Trabalho. Analisa, inicialmente, os impactos das novas demandas trabalhistas e das modernas teorias do Direito Processual no Direito Processual do Trabalho. Aborda o ônus da prova em seus aspectos gerais, definindo conceito de prova, conceitos e distinções entre ônus, obrigação e dever e conceito de ônus da prova, analisando a evolução teórica e o perfil dogmático da distribuição do ônus da prova, a estrutura funcional do ônus da prova (ônus da prova subjetivo e ônus da prova objetivo), o ônus da prova de fato negativo, a prova diabólica, a inversão judicial do ônus da prova (com ênfase para a regra prevista no Código de Defesa do Consumidor e o momento processual adequado para tanto) e a relação entre presunções, responsabilidade civil objetiva e o ônus da prova. Estuda aspectos gerais acerca do ônus da prova no Direito Processual do Trabalho, referentes à regra do artigo 818 da Consolidação das Leis do Trabalho, e a aplicação subsidiária do artigo 333 do Código de Processo Civil, e à inversão judicial do ônus da prova no processo juslaboral, com base na aplicação do Código de Defesa do Consumidor, do princípio protetor, do princípio da pré-constituição da prova e do princípio da aptidão para a prova. Analisa aspectos gerais referentes à teoria da distribuição dinâmica do ônus da prova, estabelecendo conceitos e distinções entre distribuição estática, inversão judicial e distribuição dinâmica do ônus da prova, abordando origens históricas e incorporação da teoria no Direito Comparado, fundamentos para aplicação da dinamização da carga probatória no Direito Processual Brasileiro (com ênfase ao direito fundamental à prova, ao princípio da igualdade material no processo, exercício dos poderes instrutórios do juiz, busca da verdade real e regra do artigo 333, parágrafo único, inciso II, do Código de Processo Civil) e incorporação legislativa da teoria no Direito Processual Brasileiro, prevista no Anteprojeto de Código Brasileiro de Processos Coletivos, Projeto de Lei da Ação Civil Pública e Projeto de Código de Processo Civil. Por fim, estuda especificamente a aplicação da teoria da distribuição dinâmica do ônus da prova no Direito Processual do Trabalho, partindo dos fundamentos para sua incidência no processo juslaboral (direito fundamental à prova, princípio da igualdade material no processo e a regra do artigo 852 - D da Consolidação das Leis do Trabalho), abordando critérios objetivos para a aplicação (subsidiariedade, utilização dos poderes instrutórios e das máximas de experiência do juiz, vedação do incentivo ao comodismo processual e à instauração da probatio diabólica reversa, com observância do binômio impossibilidade/extrema dificuldade do empregado na produção da prova-possibilidade/maior facilidade na produção para o empregador, fundamentação da decisão, vedação da carga processual superveniente), momento processual adequado para a dinamização, relação entre nulidades processuais e distribuição dinâmica, instrumento processual cabível para impugnação da incidência da teoria, definição da regra de distribuição do ônus da prova pelos Tribunais e casuísticas de aplicação da distribuição dinâmica do ônus da prova, com exame crítica da doutrina e da jurisprudência, no Direito Processual Individual do Trabalho (abordando os seguintes temas: jornada de trabalho, vale-transporte, equiparação salarial, depósitos do fundo de Garantia do Tempo de Serviço (FGTS), despedimento, salário-família, acidente do trabalho, assédio moral e assédio sexual, discriminação das relações de trabalho, privacidade e intimidade do trabalhador, responsabilidade subsidiária da Administração Pública, grupo econômico, sucessão trabalhista, bem de família e gratuidade processual) e no Direito Processual Coletivo do Trabalho, com formulação de proposta legislativa ao final do estudo. / This work studies the application of the theory of dynamic distribution of the burden of proof on Labor Procedural Law. It examines, initially, the impact of new labor demands and modern theories of the Procedural Law on Labor Procedural Law. It boards the burden of proof in its general aspects, defining concept of proof, concepts and distinctions between burden, obligation and duty and concept of burden of proof, analyzing the theoretical evolution and dogmatic profile of the distribution of the burden of proof, the functional structure of the burden of proof (subjective burden of proof and objective burden of proof), the burden of proof in fact negative, diabolical proof, the judicial reverse of the burden of proof (with emphasis on the rule laid down in the Consumer Defense Code and the appropriate procedural moment for this) and the relation between presumptions, strict liability and burden of proof. It studies general aspects about the burden of proof on Labor Procedural Law, referring to the rule of Artic le 818 of the Consolidation of Labor Laws, and the subsidiary application of Article 333 of the Code of Civil Procedure, and the judicial reverse of the burden of proof in Labor Procedure Law based on implementation of the Code of Consumer Protection, protective principle, principle of pre-establishment of proof and principle of the aptitude for proof. It analyzes general aspects concerning the theory of dynamic distribution of the burden of proof, establishing concepts and distinctions between static distribution, judicial reversal and dynamic distribution of the burden of proof, addressing historical origins and incorporation of the theory in Comparative Law, grounds for implementation of dynamic distribution of the burden of proof on Brazilian Procedural Law (with emphasis on the fundamental right to proof, principle of substantive equality in the process, practice of the judges investigation powers, search for real truth and rule of Article 333, sole paragraph, II, of the Code of Civil Procedure) and legislative incorporation of the theory in the Brazilian Procedural Law, foreseen in the preliminary bill of law for the Brazilian Code of Class Actions, bill of law for the Public Civil Action and bill of law for the Code of Civil Procedure. Finally, it studies specifically the application of the theory of dynamic distribution of the burden of proof on the Labor Procedural Law, starting for her impacts on the Labor Procedure (fundamental right to proof, principle of substantive equality in the process and the rule of Article 852 - D of the Consolidation of Labor Laws), addressing objective criteria to application (subsidiarity, use of the judges investigation powers, judges maxims of experience, prohibition to encourage self-indulgence and to establish reverse probatio diabolica, with observance of the binomial inability/extreme difficulty of the employee in the production of proof-possibility/ease in the production for the employer , reasons for the decision, seal to supervening procedural burden), procedural moment suitable to dynamize, relation between procedural nullity and dynamic distribution, appropriate procedural tool to challenge the incidence of the theory, definition of the distribution rule of the burden of proof by the Courts and case studies of application of the dynamic distribution of the burden of proof, with critical examination of doctrine and jurisprudence, in the Individual Labor Procedural Law (addressing the following topics: working time, transportation ticket, salary equation, Brazilian s employment compensation funds credit (FGTS), dismissal, family allowance, labor-related accident, workplace bullying and sexual harassment, discrimination in work relations, employee\'s privacy and intimacy, public administrations subsidiary liability, economic group, labor succession, homestead right and gratuity procedure) and Labor Class Actions, with formulating legislative proposition by the end of the study.

No description available.

M.Ed. / Recently there has been renewed interest in proof and proving in schools worldwide. However, many school students and even teachers of mathematics have only superficial ideas on the nature of proof. Proof is considered the heart of mathematics as individuals explore, make conjectures and try to convince themselves and others about the truth or falsity of their conjectures. There are basically two categories of deductive proof, namely proof by direct argument and indirect proofs. The aim of this study was to examine the structural features common to most of the mathematical proofs for formalised mathematical systems, with the emphasis on indirect proof techniques. The main question was to investigate which mathematical activities and logical principles at secondary school level are necessary for students to become proficient with proof writing. A great deal of specialised language is associated with reasoning. Such words as axiom, theorem, proof, and conjecture are just some of the terms that students must understand as they engage in the proof-making task. The formal aspect of mathematics at secondary school is extremely important. It is inevitable that students become involved with hypothetical arguments. They use among others, proofs by contradiction. Furthermore, necessary and sufficient conditions are related to theorems and their converses. It is therefore apparent that the study of logic is necessary already at secondary school level in order to practise mathematics satisfactorily. An analysis of the mathematics syllabus of the Department of Education has indicated that students should use indirect techniques of proof. According to this syllabus students should be familiar with logical arguments. The conclusion which is reached, gives evidence that students’ background in logic is completely lacking and inadequate. As a result they cannot cope adequately with argumentation and this causes a poor perception of what mathematics entails. Although proof writing can never be reduced to a mechanical process, considerable anxiety and uncertainty can be eliminated from the process if students are exposed to the principles of elementary logic and techniques. Mathematics educators and education researchers have reported students’ difficulties with mathematical proof and point out the conflict between the nature of this essential mathematical activity and current approaches to teaching it. This recent interest has led to an increased effort to teach proof in innovative ways.

Proof-carrying code is an application of software verification techniques to the problem of ensuring the safety of mobile code. However, previous proof-carrying code systems have assumed that mobile code will faithfully execute the instructions of the program. Realistic implementations of computing systems are susceptible to probabilistic behaviours that can alter the execution of a program in ways that can result in corruption or security breaches. We investigate the use of a probabilistic bytecode language to model deterministic programs that are executed on probabilistic computing systems. To model probabilistic safety properties, a probabilistic logic is adapted to out bytecode instruction language, and soundness is proven. A sketch of a completeness proof of the logic is also shown.

This dissertation reports on an investigation of transition-to-proof students' understanding of proof by contradiction. A plethora of research on the construction aspect of proof by contradiction is available and suggests that the method is one of the most difficult for students to construct and comprehend. However, there is little research on the students' comprehension of proofs and, in particular, proofs by contradiction. This study aims to fill this gap in the literature. Applying the cognitive lens of Action-Process-Object-Schema (APOS) Theory to proof by contradiction, this study proposes a preliminary genetic decomposition for how a student might construct the concept `proof by contradiction' and a series of five teaching interventions based on this preliminary genetic decomposition. Data was analyzed in two ways: (1) group analysis of the first two teaching interventions to consider students' initial conceptions of the proof method and (2) case study analysis of two individuals to consider how students' understanding developed over time. The genetic decomposition and teaching interventions were then revised based on the results of the data analysis. This study concludes with implications for teaching the concept of proof by contradiction and suggestions for further research on the topic.

The Industrial Internet of Things (IIoT) is growing day by day and is implemented in many industries. The centralized architecture of an IIoT system is composed of several devices that communicate with a special device only via one link, in an instance where this one link is attacked, major problems could occur for the whole system. The solution is to decentralize the entire architecture, a feature that the implementation of blockchain technology provides. Blockchain technology uses numerous consensus algorithms and some of the consensus algorithms require a large amount of computational power , such as the proof of work consensus algorithm. The problem is that IIoT devices have limited processor performance therefore it is important to find consensus algorithms that are suitable for an IIoT system in terms of time efficiency and electricity consumption. The question then becomes, which of the following different consensus algorithms; proof of work, proof of stake and proof of authentication performs best in an IIoT environment in terms of time efficiency and electricity consumption?  This question can be answered by implementing blockchain technology using the three aforementioned consensus algorithms in an IIoT environment to see which consensus algorithm is the most time efficient and uses the smallest amount of electricity. The results showed that proof of stake was the best consensus algorithm both in terms of time efficiency and electricity consumption. / Sakernas internet inom industrin (IIoT) växer dag för dag och används i flertalet industrier. Den centraliserade arkitekturen av ett IIoT-system består av flera enheter som kommunicerar med en speciell enhet endast via en länk och detta kan skapa stora problem för hela systemet om endast denna länk attackeras. Lösningen är att decentralisera hela arkitekturen, en funktion som implementeringen av blockkedjeteknologi förser. Inom blockkedjeknologi används flertalet algoritmer och bland algoritmerna finns det flera som kräver hög processorprestanda, som t.ex proof of work algoritmen. Problemet är att IIoT-enheter har begränsad processorprestanda, och ett viktigt skäl är att hitta algoritmer som är anpassade för ett IIoT-system beträffande tidseffektivitet samt elkonsumtion. Frågan blir då, vilken av de olika konsensus algoritmerna; proof of work, proof of stake och proof of authentication presterar bäst i en IIoT-miljö sett ur tidseffektivitet och elkonsumtion?  Denna fråga kan besvaras genom att implementera blockkedjeteknologi med de tre ovannämnda algoritmer i en IIoT-miljö för att se vilken algoritm är den mest tidseffektiva och har lägst elkonsumtion. Resultatet visade att proof of stake var den bästa konsensus algoritmen både tidsmässigt och elkonsumtion mässigt.