8 resultados para Proofs

em Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland


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The objective of the dissertation is to increase understanding and knowledge in the field where group decision support system (GDSS) and technology selection research overlap in the strategic sense. The purpose is to develop pragmatic, unique and competent management practices and processes for strategic technology assessment and selection from the whole company's point of view. The combination of the GDSS and technology selection is approached from the points of view of the core competence concept, the lead user -method, and different technology types. In this research the aim is to find out how the GDSS contributes to the technology selection process, what aspects should be considered when selecting technologies to be developed or acquired, and what advantages and restrictions the GDSS has in the selection processes. These research objectives are discussed on the basis of experiences and findings in real life selection meetings. The research has been mainly carried outwith constructive, case study research methods. The study contributes novel ideas to the present knowledge and prior literature on the GDSS and technology selection arena. Academic and pragmatic research has been conducted in four areas: 1) the potential benefits of the group support system with the lead user -method,where the need assessment process is positioned as information gathering for the selection of wireless technology development projects; 2) integrated technology selection and core competencies management processes both in theory and in practice; 3) potential benefits of the group decision support system in the technology selection processes of different technology types; and 4) linkages between technology selection and R&D project selection in innovative product development networks. New type of knowledge and understanding has been created on the practical utilization of the GDSS in technology selection decisions. The study demonstrates that technology selection requires close cooperation between differentdepartments, functions, and strategic business units in order to gather the best knowledge for the decision making. The GDSS is proved to be an effective way to promote communication and co-operation between the selectors. The constructs developed in this study have been tested in many industry fields, for example in information and communication, forest, telecommunication, metal, software, and miscellaneous industries, as well as in non-profit organizations. The pragmatic results in these organizations are some of the most relevant proofs that confirm the scientific contribution of the study, according to the principles of the constructive research approach.

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The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.

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Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

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Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

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The three main topics of this work are independent systems and chains of word equations, parametric solutions of word equations on three unknowns, and unique decipherability in the monoid of regular languages. The most important result about independent systems is a new method giving an upper bound for their sizes in the case of three unknowns. The bound depends on the length of the shortest equation. This result has generalizations for decreasing chains and for more than three unknowns. The method also leads to shorter proofs and generalizations of some old results. Hmelevksii’s theorem states that every word equation on three unknowns has a parametric solution. We give a significantly simplified proof for this theorem. As a new result we estimate the lengths of parametric solutions and get a bound for the length of the minimal nontrivial solution and for the complexity of deciding whether such a solution exists. The unique decipherability problem asks whether given elements of some monoid form a code, that is, whether they satisfy a nontrivial equation. We give characterizations for when a collection of unary regular languages is a code. We also prove that it is undecidable whether a collection of binary regular languages is a code.

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The increasing use of energy, food, and materials by the growing population in the world is leading to the situation where alternative solutions from renewable carbon resources are sought after. The growing use of plastics depends on the raw-oil production while oil refining are politically governed and required for the polymer manufacturing is not sustainable in terms of carbon footprint. The amount of packaging is also increasing. Packaging is not only utilising cardboard and paper, but also plastics. The synthetic petroleum-derived plastics and inner-coatings in food packaging can be substituted with polymeric material from the renewable resources. The trees in Finnish forests constitute a huge resource, which ought to be utilised more effectively than it is today. One underutilised component of the forests is the wood-derived hemicelluloses, although Spruce Oacetyl-galactoglucomannans (GGMs) have previously shown high potential for material applications and can be recovered in large scale. Hemicelluloses are hydrophilic in their native state, which restrains the use of them for food packaging as non-dry item. To cope with this challenge, we intended to make GGMs more hydrophobic or amphiphilic by chemical grafting and consequently with the focus of using them for barrier applications. Methods of esterification with anhydrides and cationic etherification with a trimethyl ammonium moiety were established. A method of controlled synthesis to obtain the desired properties by the means of altering temperature, reaction time, the quantity of the reagent, and even the solvent for purification of the products was developed. Numerous analytical tools, such as NMR, FTIR, SEC-MALLS/RI, MALDI-TOF-MS, RP-HPLC and polyelectrolyte titration were used to evaluate the products from different perspectives and to acquire parallel proofs of their chemical structure. Modified GGMs with different degree of substitution and the correlating level of hydrophobicity was applied as coatings on cartonboard and on nanofibrillated cellulose-GGM films to exhibit barrier functionality. The water dispersibility in processing was maintained with GGM esters with low DS. The use of chemically functionalised GGM was evaluated for the use as barriers against water, oxygen and grease for the food packaging purposes. The results show undoubtedly that GGM derivatives exhibit high potential to function as a barrier material in food packaging.

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This work investigates theoretical properties of symmetric and anti-symmetric kernels. First chapters give an overview of the theory of kernels used in supervised machine learning. Central focus is on the regularized least squares algorithm, which is motivated as a problem of function reconstruction through an abstract inverse problem. Brief review of reproducing kernel Hilbert spaces shows how kernels define an implicit hypothesis space with multiple equivalent characterizations and how this space may be modified by incorporating prior knowledge. Mathematical results of the abstract inverse problem, in particular spectral properties, pseudoinverse and regularization are recollected and then specialized to kernels. Symmetric and anti-symmetric kernels are applied in relation learning problems which incorporate prior knowledge that the relation is symmetric or anti-symmetric, respectively. Theoretical properties of these kernels are proved in a draft this thesis is based on and comprehensively referenced here. These proofs show that these kernels can be guaranteed to learn only symmetric or anti-symmetric relations, and they can learn any relations relative to the original kernel modified to learn only symmetric or anti-symmetric parts. Further results prove spectral properties of these kernels, central result being a simple inequality for the the trace of the estimator, also called the effective dimension. This quantity is used in learning bounds to guarantee smaller variance.