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ConstruÃÃes dos nÃmeros reais voltadas para os professores da rede bÃsica de ensino / Construction of real numbers facing teachers of basic network of educationFernando AraÃjo Ribeiro 11 June 2015 (has links)
CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / Este trabalho tem como objetivo mostrar que o conjunto dos nÃmeros reais à um corpo ordenado completo e que, a menos de um isomorfismo, à Ãnico. Este trabalho à voltado para todos aqueles que tenham interesse em MatemÃtica, sobretudo, para os professores de MatemÃtica do ensino mÃdio que utilizam as propriedades do conjunto dos nÃmeros reais sem conhecer a teoria matemÃtica envolvida. Para tanto, à necessÃrio caracterizar o conjunto dos reais a fim de provar suas propriedades. Aqui, utilizamos duas construÃÃes, a saber: os reais via sequÃncias de Cauchy devido a Cantor e os reais via Cortes de Dedekind. A partir dessas caracterizaÃÃes, conseguimos construir um corpo K munido das operaÃÃes de soma e multiplicaÃÃo onde mostramos que ele cumpre as condiÃÃes da definiÃÃo de corpo. Definida uma relaÃÃo de ordem em K, mostramos que tal corpo à ordenado e, alÃm disso, conseguimos mostrar que todo subconjunto de K admite supremo, o que quer dizer que tal corpo à completo. Finalmente, mostramos que qualquer outro corpo ordenado completo que possa, por ventura, existir à uma mera caracterizaÃÃo de ℝ, o que quer dizer que ℝ à Ãnico, a menos dessas possÃveis outras caracterizaÃÃes. Tal caracterizaÃÃo serà chamada de isomorfismo que à uma funÃÃo bijetora de ℝ para K. / This work aims to show that the set of real numbers is a complete ordered field that, within an isomorphism, is unique. This work is aimed at all those who are interested in mathematics, especially for that high school math teacher who uses the real numbers of the set of properties without knowing the mathematical theory involved. Therefore, it is necessary to characterize the set of the real in order to prove their properties. Here, we use two buildings, namely: the real via Cauchy sequences due to Cantor and the real via Dedekind cuts. From these characterizations, we can build a field K equipped with the addition and multiplication operations which show that it meets the definition of field conditions. Set an order relation in K, we show that such a body is ordered and in addition, we show that every subset of K admits supreme, which means that such a field is complete. Finally, we show that any complete ordered field that can, perchance appear is a mere characterization of ℝ, which means that ℝ is unique, unless these possible other characterizations. This characterization will be called isomorphism which is a function bijetora of ℝ to K.
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Números reais: um corpo ordenado e completo / Real numbers: a complete ordered fieldSouza, Jadson da Silva 22 March 2013 (has links)
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Previous issue date: 2013-03-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper aims to expand knowledge about the real numbers, providing a new perspective
on their conceptual construction. Initially, covers up some historical facts that were of
utmost importance in the process of conceptual evolution of the real numbers. Secondly,
through the development of theories of abstract algebra, sets and mathematical analysis, is
used a axiomatic method to expose the complete ordered field of real, stating and proving
some of its properties. Finally, we discuss some relevant aspects of the correspondence
between the real field and line, and also the correspondence between the real field and
decimals. / Este trabalho tem como objetivo ampliar os conhecimentos sobre os números reais,
proporcionando uma nova perspectiva sobre sua construção conceitual. Inicialmente,
aborda-se alguns fatos históricos que foram de maior importância no processo da evolução
conceitual dos números reais. Posteriormente, por meio do desenvolvimento das teorias de
álgebra, de conjuntos e de análise matemática, utiliza-se de um método axiomático para
expor uma construção do corpo ordenado e completo dos reais, enunciando e provando
algumas de suas propriedades. Finalmente, abordam-se alguns aspectos relevantes da
correspondência entre o corpo dos reais e a reta, e ainda da correspondência entre o corpo
dos reais e os decimais.
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Candidose associada ao uso de prótese total superior: avaliação demográfica, clínica e microscópica / Candidosis associated with the use of maxillary complete denture: demographic, clinical and microscopic evaluationErika Martins Pereira 03 April 2007 (has links)
A estomatite por dentadura representa um processo inflamatório na mucosa oral em contato com a resina acrílica da prótese total ou parcial removível, sendo sua etiologia multifatorial, associada com fatores locais e sistêmicos, incluindo a presença de Candida albicans. O presente trabalho teve como objetivo a realização de uma análise demográfica, clínica e microscópica da candidose, associada ao uso da prótese total superior, nas formas atrófica, hiperplásica papilar e associada à hiperplasia fibrosa inflamatória. Para este fim, as amostras dos arquivos do laboratório de Anatomia Patológica do Departamento de Estomatologia - Área de Patologia - da Faculdade de Odontologia de Bauru, da Universidade de São Paulo, foram avaliadas microscopicamente, por meio das colorações de Hematoxilina e Eosina, Grocott de prata e Periodic Acid Schiffer (PAS), em comparação à mucosa normal de palato, oriunda de pacientes não usuários de prótese total ou removível superior. Foram resgatadas todas as informações contidas nas fichas clínicas correspondentes às amostras. As amostras de candidose bucal, independente do grupo, foram provenientes principalmente de indivíduos idosos, com médias variando de 51 a 60 anos, do gênero feminino e raça branca. Em alguns casos, o diagnóstico clínico da estomatite por dentadura atrófica pode ser difícil, necessitando de biópsia para confirmação. As lesões de hiperplasia papilar são removidas cirurgicamente com mais freqüência que aquelas de estomatite por dentadura atrófica, sendo geralmente reconhecidas pelo profissional clínico como hiperplasia fibrosa inflamatória. A candidose nas hiperplasias fibrosas inflamatórias não apresenta sinais clínicos exclusivos da sua presença; assim, torna-se improvável a suspeita clínica desta associação. De forma diferente da mucosa normal, microscopicamente, na maioria dos casos de candidose bucal, observaram-se revestimento epitelial hiperplásico com cristas alongadas, algumas em forma de tubo de ensaio, com freqüentes áreas de ausência de queratina, pequenos focos de reação liquenóide e de microabscessos, bem como extensas áreas de hiperplasia pseudoepiteliomatosa. Somente a hiperplasia papilar apresentou cristas epiteliais bífidas, revelando ainda maior freqüência de pérolas córneas-like e cristas em forma de tubo de ensaio, quando comparada com as outras formas de candidose bucal. O tecido conjuntivo fibroso subjacente, na candidose bucal, revelou intenso a moderado infiltrado inflamatório mononuclear predominante na lâmina própria e região perivascular. Não se observou marcação fúngica por meio das colorações especiais Grocott de prata e PAS. Assim, o diagnóstico microscópico da candidose bucal não deve depender da visualização do fungo nas camadas mais superficiais do revestimento epitelial. / Denture stomatitis is an inflammatory process affecting the oral mucosa in contact with acrylic resin of complete dentures or removable partial dentures. The disease has a multifactorial etiology, associate with local and systemic factors, including the presence of Candida albicans. The present study aimed to conduct a demographic, clinical and microscopic analysis of candidosis associated with the use of maxillary complete denture, in both atrophic and papillary hyperplastic forms and associated with inflammatory fibroepithelial hyperplasia. For that purpose, specimens from the files of the Anatomical Pathology Laboratory at the Department of Stomatology, Bauru Dental School, University of São Paulo, were microscopically reviewed in sections stained with hematoxylin and eosin (HE), Grocott\'s methenamine silver and periodic acid-Schiff (PAS), and compared to normal palatal tissues obtained from non-denture wearers. Clinical information was obtained and selected from clinical records. Regardless of the group, the specimens of oral candidosis were mainly obtained from aged individuals, with average age of 51 to 60 years, especially females and white individuals. In some cases, the clinical diagnosis of the atrophic denture stomatitis can be difficult and requires biopsy for confirmation. Papillary hyperplasia lesions are removed more frequently than atrophic denture stomatitis lesions, since they are generally recognized by clinicians as inflammatory fibroepithelial hyperplasia. Candidosis in inflammatory fibroepithelial hyperplasia does not present exclusive clinical signs of its presence; thus, clinical suspicion of this association is improbable. Different from the normal mucosa, microscopically, most cases of oral candidosis present hyperplastic epithelial lining with elongated rete pegs, some with \"test tube\" aspect, with frequent areas of absence of keratin, small foci of lichenoid reaction and microabscesses, as well as extensive areas of pseudoepitheliomatous hyperplasia. Only papillary hyperplastic lesions exhibited bifid rete pegs, besides high frequency of keratin pearls-like and long \"test tube\" rete pegs, when compared with the other forms of oral candidosis. The connective tissue underlying the oral candidosis presented moderate to intense mononuclear inflammatory infiltrate, predominantly at the lamina propria and perivascular region. Fungal hyphae and yeasts were not identified by special staining with Grocott\'s methenamine silver and (PAS). Thus, the microscopic diagnosis of oral candidosis should not depend on the visualization of fungal hyphae and yeasts at the most superficial layers of epithelial li pegs, when compared with the other forms of oral candidosis. The connective tissue underlying the oral candidosis presented moderate to intense mononuclear inflammatory infiltrate, predominantly at the lamina propria and perivascular region. Fungal hyphae and yeasts were not identified by special staining with Grocott\'s methenamine silver and (PAS). Thus, the microscopic diagnosis of oral candidosis should not depend on the visualization of fungal hyphae and yeasts at the most superficial layers of epithelial lining.
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Avaliação in vitro da ação do hipoclorito de sódio e de pastilhas efervescentes quanto à alteração de cor em resinas acrílicas termopolimerizáveis e de microondas / In vitro evaluation of sodium hypochlorite and effervescent tablets actionregarding color alteration of heat and microwave-polymerized acrylic resinsAmanda Peracini 10 July 2008 (has links)
O objetivo deste estudo foi avaliar a alteração de cor de resinas acrílicas termopolimerizáveis (convencional e de microondas) após imersões em soluções químicas higienizadoras de próteses totais em diferentes períodos de tempo. Foram obtidos padrões em cera (15mm de diâmetro e 4mm de espessura), a partir de uma matriz de teflon, que foram incluídos em muflas convencionais e para microondas. Após a eliminação da cera, as resinas foram manipuladas, prensadas e polimerizadas segundo as instruções dos fabricantes. Foram confeccionados 200 corpos-de-prova, 100 de cada marca comercial das resinas Lucitone 550 (L) e Onda Cryl (OC), os quais foram imersos nas soluções: A)Água destilada-3 min.; B)Bony Plus -3 min.; C)Água destilada-5 min.; D)Corega Tabs-5 min.; E)Água destilada-20 min.; F)Hipoclorito de sódio a 0,5%-20 min.; G)Hipoclorito de sódio a 1%-20 min.; H)Água destilada-8 horas; I)Hipoclorito de sódio a 0,5%-8 horas; J)Hipoclorito de sódio a 1%-8 horas. A alteração de cor foi avaliada empregando-se um espectrocolorímetro (Color Guide 45/0 BYK-Gardner) antes e após a simulação de 180 dias de imersão. Os resultados foram comparados por meio da análise de variância (ANOVA) para dois fatores, seguida pelo teste de Student-Newman Keuls, com nível de significância de 0,05. Para correlacionar as diferenças de cor para o ambiente clínico, os dados foram calculados de acordo com as unidades da National Bureau of Standards (NBS). Os resultados mostraram que a resina Lucitone 550 (ΔE = 0,47±0,18) apresentou-se mais estável que a Onda-Cryl (ΔE = 0,53±0,31). Para ambas as resinas, as pastilhas, os hipocloritos por 20 minutos (0,5% e 1%) e por 08 horas (0,5%) não provocaram alterações maiores que seus respectivos controles (L-A: 0,27 ±0,10; L-B: 0,44±0,21; L-C: 0,48±0,21; L-D: 0,46±0,13; L-E: 0,29±0,07; L-F: 0,37±0,08; L-G: 0,47±0,10; L-H: 0,61±0,11; L-I: 0,55±0,10; OC-A: 0,22±0,08; OC-B: 0,43±0,32; OC-C: 0,65±0,35; OC-D: 0,41±0,11; OC-E: 0,31±0,11; OC-F: 0,29±0,07; OC-G: 0,37 ±0,11; OC-H: 0,78±0,10; OC-I: 0,79±0,08). As soluções de hipoclorito a 1% (L-J: 0,74±0,09; OC-J: 1,06 ±0,13) causaram maiores alterações que seus respectivos controles. As soluções empregadas por 08 horas (água e Hipocloritos a 0,5% e 1%) provocaram alterações classificadas como leves, segundo o sistema NBS. Os achados deste estudo revelaram que as pastilhas efervescentes, quando usadas de acordo com as instruções dos fabricantes, e o hipoclorito de sódio (0,5% e 1%) por 20 minutos apresentaram menores valores de alteração de cor nas resinas acrílicas após um período de uso simulado de 180 dias. Médias mais elevadas foram obtidas quando um regime de 8 horas foi simulado. / The aim of this study was to evaluate color alteration of heat-polymerized acrylic resins (conventional and microwave-polymerized), after immersion in chemicals solutions of denture cleansers for different periods of time. Wax patterns were obtained (15 mm in diameter and 4 mm thickness) from a teflon matrix and were invested in metallic or microwavable flasks. The wax had been eliminated and the resins were mixed, packed and polymerized according to the manufacturers instructions. Two hundred specimens were made, 100 specimens of each commercial resin Lucitone 550 (L) e Onda Cryl (OC), which were immersed in the solutions: A)Distilled water-3 min.; B)Bony Plus-3 min.; C)Distilled water-5 min.; D)Corega Tabs-5 min.; E) Distilled water -20 min.; F) 0,5% Sodium Hypochlorite-20 min.; G) 1% Sodium Hypochlorite-20 min.; H)Distilled water-8 hours; I)0,5% Sodium Hypochlorite-8 hours; J)1% Sodium Hypochlorite -8 hours. Color alteration was assessed by a spectrocolorimeter (Color Guide 45/0 (BYKGardner) before and after 180 days simulation. The results were analyzed statistically by a two-way analysis of variance (ANOVA), and Student Newman-Keuls test, with significance level of 0.05. To relate the color differences to a clinical environment, the data were quantified by National Bureau of Standards (NBS) units. The results showed that the resin Lucitone 550 (ΔE=0,47±0,18) was more stable than the resin Onda-Cryl (ΔE=0,53±0,31). For both resins, the tablets, the hypochlorite by 20 minutes (0,5% e 1%) and by 8 hours (0,5%) did not produce higher alterations than the respective controls (L-A: 0,27 ±0,10; L-B: 0,44±0,21; L-C: 0,48±0,21; L-D: 0,46±0,13; L-E: 0,29±0,07; L-F: 0,37±0,08; L-G: 0,47±0,10; L-H: 0,61±0,11; L-I: 0,55±0,10; OC-A: 0,22±0,08; OC-B: 0,43±0,32; OC-C: 0,65±0,35; OC-D: 0,41±0,11; OC-E: 0,31±0,11; OC-F: 0,29±0,07; OC-G: 0,37 ±0,11; OC-H: 0,78±0,10; OC-I: 0,79±0,08). The 1% hypochlorite solutions (L-J: 0,74±0,09; OC-J: 1,06 ±0,13) produced higher alterations than the respective controls. The solutions employed by 8 hours (water and 0,5% and 1% hipochlorite) produced alterations classified as slight, according to the NBS system. The findings of this study showed that the effervescent tablets, used according to the manufacturer´s instructions, and the sodium hypochlorite (0,5% and 1%) used by 20 minutes presented lower values of color alterations in acrylic resins after a period of 180 days simulation. Higher mean averages were obtained when a period of 8 hours was simulated.
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Elaboração de marcadores pedagógicos como subsídio para construção de projeto político pedagógico para o ensino superior em enfermagemMix, Paulo Roberto 15 June 2016 (has links)
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Previous issue date: 2016-06-15 / Nenhuma / Este texto é resultado de um estudo de natureza qualitativa, exploratório, descritivo. Que teve como objetivo de Propor marcadores pedagógicos que subsidiem a elaboração de um Projeto Político Pedagógico (PPP) para um curso de graduação em enfermagem no Município de Santa Rosa. Os dados foram coletados utilizando a técnica de Grupo Focal, que teve como dispositivo para sua composição o Quadrilátero da Formação para área da saúde, com participantes da área do ensino, da gestão, da atenção e do controle social, com total de oito participantes que representaram as quatro faces do quadrilátero. Foram realizadas três sessões resultaram com a indicação de quatro marcadores pedagógicos afetos a formação do enfermeiro que foram: Compromisso com o SUS, Integralidade da atenção à saúde, Responsabilização nos processos de cuidado em saúde e Gerenciamento e Liderança. Apresentamos uma proposta de matriz curricular que servirá de sugestão para a implementação de um Curso de Enfermagem na perspectiva de reforçar o compromisso social e político e atender as exigências de novos modelos de formação no ensino superior. Para que seja possível um novo modo de formação de enfermeiros, a proposta da matriz em tela tem essa intenção, é premente a orientação desse processo formativo através das necessidades de saúde da população, com integração do ensino com serviço efetiva e bidirecional, construindo um alicerce sólido para transformação das práticas de atenção e do processo de trabalho e entendendo de que de fato a integralidade será uma realidade na atenção quando compreendermos o usuário e seus problemas como centro da atenção à saúde / The objective of this qualitative study is to propose pedagogical markers that support the development of a pedagogical political project (PPP) for a degree course in nursing in the municipality of Santa Rosa. The data were collected using the focus group technique, which in turn utilized the square formation device for health, including participants from the areas of education, management, and social control; a total of eight participants represented the four sides of the square. Three sessions were held, the audio was recorded and subsequently transcribed, and the content analysis technique was used to analyze the data. Four pedagogical markers that affect the training of nurses emerged: Commitment to the SUS [Brazilian Unified Health Care System], Completeness of attention to health, Accountability in health care processes, and Management and leadership. Here we present a proposal for a base curriculum that will serve as a suggestion for implementing a nursing course from the perspective of reinforcing political and social commitment and meeting the requirements of new training models for higher education. In order for the proposed base curriculum to allow a new training mode for nurses, it is fundamental that this training process be guided by the health needs of the population, be integrated into the training with effective and two-way service, constructing a solid foundation to transform care practices and the work process, while understanding that complete care will truly be a reality once we understand the users and their problems as the center of health care.
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Complete-MDP convolutional codes over the erasure channelTomás Estevan, Virtudes 20 July 2010 (has links)
No description available.
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Finiteness of Complete Intersection Calabi Yau ThreefoldsPassaro, Davide January 2019 (has links)
Of many modern constructions in geometry Calabi Yau manifolds hold special relevance in theoretical physics. These manifolds naturally arise from the study of compactification of certain string theories. In particular Calabi Yau manifolds of dimension three, commonly known as threefolds, are widely used for compactifications of heterotic string theories. Among the many constructions, that of complete intersection Calabi Yau manifolds (CICY) is generally regarded to be the simplest. Furthermore, CICY threefolds have been proven to exist only in finite number. In the following text CICY manifolds will be analyzed, with particular attention to threefolds. A general description of some of their topological quantities and their calculation is offered. Lastly, a proof of the finiteness of CICY threefolds is given.
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Generalized factorization in commutative rings with zero-divisorsMooney, Christopher Park 01 July 2013 (has links)
The study of factorization in integral domains has a long history. Unique factorization domains, like the integers, have been studied extensively for many years. More recently, mathematicians have turned their attention to generalizations of this such as Dedekind domains or other domains which have weaker factorization properties. Many authors have sought to generalize the notion of factorization in domains. One particular method which has encapsulated many of the generalizations into a single study is that of tau-factorization, studied extensively by A. Frazier and D.D. Anderson.
Another generalization comes in the form of studying factorization in rings with zero-divisors. Factorization gets quite complicated when zero-divisors are present due to the existence of several types of associate relations as well as several choices about what to consider the irreducible elements.
In this thesis, we investigate several methods for extending the theory of tau-factorization into rings with zero-divisors. We investigate several methods including: 1) the approach used by A.G. Agargun and D.D. Anderson, S. Chun and S. Valdes-Leon in several papers; 2) the method of U-factorization developed by C.R. Fletcher and extended by M. Axtell, J. Stickles, and N. Baeth and 3) the method of regular factorizations and 4) the method of complete factorizations.
This thesis synthesizes the work done in the theory of generalized factorization and factorization in rings with zero-divisors. Along the way, we encounter several nice applications of the factorization theory. Using tau_z-factorizations, we discover a nice relationship with zero-divisor graphs studied by I. Beck as well as D.D. Anderson, D.F. Anderson, A. Frazier, A. Lauve, and P. Livingston. Using tau-U-factorization, we are able to answer many questions that arise when discussing direct products of rings.
There are several benefits to the regular factorization factorization approach due to the various notions of associate and irreducible coinciding on regular elements greatly simplifying many of the finite factorization property relationships. Complete factorization is a very natural and effective approach taken to studying factorization in rings with zero-divisors. There are several nice results stemming from extending tau-factorization in this way. Lastly, an appendix is provided in which several examples of rings satisfying the various finite factorization properties studied throughout the thesis are given.
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Edge-transitive homogeneous factorisations of complete graphsLim, Tian Khoon January 2004 (has links)
[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] This thesis concerns the study of homogeneous factorisations of complete graphs with edge-transitive factors. A factorisation of a complete graph Kn is a partition of its edges into disjoint classes. Each class of edges in a factorisation of Kn corresponds to a spanning subgraph called a factor. If all the factors are isomorphic to one another, then a factorisation of Kn is called an isomorphic factorisation. A homogeneous factorisation of a complete graph is an isomorphic factorisation where there exists a group G which permutes the factors transitively, and a normal subgroup M of G such that each factor is M-vertex-transitive. If M also acts edge-transitively on each factor, then a homogeneous factorisation of Kn is called an edge-transitive homogeneous factorisation. The aim of this thesis is to study edge-transitive homogeneous factorisations of Kn. We achieve a nearly complete explicit classification except for the case where G is an affine 2-homogeneous group of the form ZR p x G0, where G0 is less than or equal to ΓL(1,p to the power of R). In this case, we obtain necessary and sufficient arithmetic conditions on certain parameters for such factorisations to exist, and give a generic construction that specifies the homogeneous factorisation completely, given that the conditions on the parameters hold. Moreover, we give two constructions of infinite families of examples where we specify the parameters explicitly. In the second infinite family, the arc-transitive factors are generalisations of certain arc-transitive, self-complementary graphs constructed by Peisert in 2001.
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Improvements to Clause Weighting Local Search for Propositional SatisfiabilityFerreira Junior, Valnir, N/A January 2007 (has links)
The propositional satisfiability (SAT) problem is of considerable theoretical and practical relevance to the artificial intelligence (AI) community and has been used to model many pervasive AI tasks such as default reasoning, diagnosis, planning, image interpretation, and constraint satisfaction. Computational methods for SAT have historically fallen into two broad categories: complete search and local search. Within the local search category, clause weighting methods are amongst the best alternatives for SAT, becoming particularly attractive on problems where a complete search is impractical or where there is a need to find good candidate solutions within a short time. The thesis is concerned with the study of improvements to clause weighting local search methods for SAT. The main contributions are: A component-based framework for the functional analysis of local search methods. A clause weighting local search heuristic that exploits longer-term memory arising from clause weight manipulations. The approach first learns which clauses are globally hardest to satisfy and then uses this information to treat these clauses differentially during weight manipulation [Ferreira Jr and Thornton, 2004]. A study of heuristic tie breaking in the domain of additive clause weighting local search methods, and the introduction of a competitive method that uses heuristic tie breaking instead of the random tie breaking approach used in most existing methods [Ferreira Jr and Thornton, 2005]. An evaluation of backbone guidance for clause weighting local search, and the introduction of backbone guidance to three state-of-the-art clause weighting local search methods [Ferreira Jr, 2006]. A new clause weighting local search method for SAT that successfully exploits synergies between the longer-term memory and tie breaking heuristics developed in the thesis to significantly improve on the performance of current state-of-the-art local search methods for SAT-encoded instances containing identifiable CSP structure. Portions of this thesis have appeared in the following refereed publications: Longer-term memory in clause weighting local search for SAT. In Proceedings of the 17th Australian Joint Conference on Artificial Intelligence, volume 3339 of Lecture Notes in Artificial Intelligence, pages 730-741, Cairns, Australia, 2004. Tie breaking in clause weighting local search for SAT. In Proceedings of the 18th Australian Joint Conference on Artificial Intelligence, volume 3809 of Lecture Notes in Artificial Intelligence, pages 7081, Sydney, Australia, 2005. Backbone guided dynamic local search for propositional satisfiability. In
Proceedings of the Ninth International Symposium on Artificial Intelligence and Mathematics, AI&M, Fort Lauderdale, Florida, 2006.
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