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Modelo matricial para la construcción del diagrama de hasse de un conjunto parcialmente ordenadoAcosta De la Cruz, Pedro Raúl 31 July 2017 (has links)
El trabajo de investigación tuvo como objetivo el diseño de un modelo matricial para la construcción del diagrama de Hasse de un Conjunto Parcialmente Ordenado (CPO), que permita su implementación en un lenguaje de programación. Para lograrlo se utilizó la teoría de Relaciones de Orden Parcial, sus propiedades; matrices booleanas, sus operaciones. Este trabajo permitió determinar el diagrama de Hasse de Relaciones de Orden Parcial sin importar la cantidad de elementos del CPO, y lo más importante, permitió automatizar el modelo. / The research work was aimed at the design of a matrix model for the construction of the Hasse diagram of a Partially Ordained Set (CPO), which allows its implementation in a programming language. To achieve this, we used the theory of partial order relations, their properties; Boolean matrices, their operations. This work allowed to determine the Hasse diagram of Partial Order Relations regardless of the number of elements of the CPO, and most importantly, allowed to automate the model.
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Degree Sequences, Forcibly Chordal Graphs, and Combinatorial Proof SystemsAltomare, Christian J. January 2009 (has links)
No description available.
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Two Problems in Computational GenomicsBelal, Nahla Ahmed 22 March 2011 (has links)
This work addresses two novel problems in the field of computational genomics. The first is whole genome alignment and the second is inferring horizontal gene transfer using posets. We define these two problems and present algorithmic approaches for solving them. For the whole genome alignment, we define alignment graphs for representing different evolutionary events, and define a scoring function for those graphs. The problem defined is proven to be NP-complete. Two heuristics are presented to solve the problem, one is a dynamic programming approach that is optimal for a class of sequences that we define in this work as breakable arrangements. And, the other is a greedy approach that is not necessarily optimal, however, unlike the dynamic programming approach, it allows for reversals. For inferring horizontal gene transfer, we define partial order sets among species, with respect to different genes, and infer genes involved in horizontal gene transfer by comparing posets for different genes. The posets are used to construct a tree for each gene. Those trees are then compared and tested for contradiction, where contradictory trees correspond to genes that are candidates of horizontal gene transfer. / Ph. D.
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Halbordnungsbasierte Verfeinerung zur Verifikation verteilter AlgorithmenPeuker, Sibylle 03 July 2001 (has links)
In dieser Arbeit geht es um die schrittweise Verfeinerung verteilter Algorithmen. Dabei wird ein einfacher Algorithmus, der einige gewünschte Eigenschaften hat, Schritt für Schritt zu einem komplexen Algorithmus verfeinert, der konkrete Implementationsanforderungen erfüllt, so daß in jedem Schritt die gewünschten Eigenschaften erhalten bleiben. Wir stellen einen neuen eigenschaftserhaltenden Verfeinerungsbegriff vor, der auf der kausalen Ordnung der Aktionen eines Algorithmus basiert. Diesen Begriff definieren wir als Transitionsverfeinerung für elementare Petrinetze und diskutieren Beweiskriterien. Danach definieren und diskutieren wir die simultane Verfeinerung mehrerer Transitionen. Zur Modellierung komplexer verteilter Algorithmen sind elementare Petrinetze oft nicht adäquat. Wir benutzen deshalb algebraische Petrinetze. Wir definieren Transitionsverfeinerung für algebraische Petrinetze und stellen einen Zusammenhang zur simultanen Verfeinerung von Transitionen in elementaren Petrinetzen her. Transitionsverfeinerung ist besonders für Verfeinerungsschritte geeignet, in denen synchrone Kommunikation zwischen Agenten durch asynchronen Nachrichtenaustausch ersetzt wird. Wir zeigen dies am Beispiel eines komplexen verteilten Algorithmus, zur Berechnung des minimalen spannenden Baumes in einem gewichteten Graphen. Wir zeigen die Korrektheit dieses Algorithmus in mehreren Schritten, von denen einige Schritte Transitionsverfeinerungen sind. In anderen Schritten sind klassische Verfeinerungsbegriffe ausreichend. Wir übertragen deshalb auch einen klassischen Verfeinerungsbegriff in unser formales Modell. / The topic of this PhD thesis is the stepwise refinement of distributed algorithms. Stepwise refinement starts with a simple algorithm with certain desired properties. This algorithm is refined step by step such that the desired properties are preserved in each refinement step. The result is a complex distributed algorithm which satisfies concrete implementation requirements and which still has the desired properties. We propose a new property preserving notion of refinement which is based on the causal ordering of actions of an algorithm. We call this notion transition refinement and we define it first for elementary Petri nets. Furthermore, we discuss proof criteria. Then, we define and discuss the simultaneous refinement of several transitions. For modelling complex distributed algorithms, we use algebraic Petri nets instead of elementary Petri nets. We define transition refinement for algebraic Petri nets, and we show its relationship to simultaneous transition refinement in elementary Petri nets. Transition refinement is particularly suitable for refinement steps in which synchronous communication between agents is replaced by asynchronous message passing. We show this by means of a complex distributed algorithm for determining the minimal spanning tree of a weighted graph. We prove the correctness of this algorithm in several steps. Some of these steps are transition refinements. For other steps, well-known notions of refinement are sufficient. Therefore, we also carry over a well-known notion of refinement into our formal model.
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Unfolding based verification of concurrent infinite-state systemsTrần, Thế Quang 19 June 2009 (has links)
Nous proposons une technique de dépliage pour vérifier les systèmes concurrents infinis bien structurés. Certaines propriétés d'intérêt comme la bornitude, la couverture et la terminaison sont décidables grâce à la bonne structure de ces systèmes. D'autre part, le dépliage réduit efficacement l'explosion combinatoire en exploitant l'ordre partiel entre les événements des systèmes concurrents. Nous proposons une modélisation par structure d'événements pour des systèmes bien structurés élémentaires, tels les compteurs et les files de communication. Le dépliage d'un réseau de structures d'événements étant une structure d'événements, nous proposons ensuite une approche hiérarchique à la modélisation et à la vérification des systèmes, qui préserve la bonne structure. Enfin, nous proposons une technique d'élimination des événements redondants. La mise en œuvre de notre approche dans l'outil ESU nous permet de conclure à son efficacité. / We propose an unfolding technique for verifying concurrent infinite-state systems that are well-structured. Some properties of interest such as boundedness, coverability and termination are decidable thanks to the well-structure of these systems. Moreover, the unfolding effectively reduces the combinatorial explosion by exploiting the partial order between events of concurrent systems. We propose a modelization using event structures for basic well-structured systems, such as counters and communication channels. As the unfolding of a synchronized product of event structures is an event structure, we obtain a hierarchical approach to modeling as well as to verifying systems, which preserves the well-structure. Finally, we propose a technique for eliminating redundant events. The implementation of our approach in the ESU tool allows us to conclude on its efficiency.
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Modeling and Performance Analysis of Distributed Systems with Collaboration Behaviour DiagramsIsrar, Toqeer 23 April 2014 (has links)
The use of distributed systems, involving multiple components, has become a common industry practice. However, modeling the behaviour of such systems is a challenge, especially when the behavior consists of several collaborations of different parties, each involving possibly several starting (input) and ending (output) events of the involved components. Furthermore, the global behavior should be described as a composition of several sub-behaviours, in the following called collaborations, and each collaboration may be further decomposed into several sub-collaborations. We assume that the performance of the elementary sub-collaborations is known, and that the performance of the global behavior should be determined from the performance of the contained elementary collaborations and the form of the composition.
A collaboration, in this thesis, is characterized by a partial order of input and output events, and the performance of the collaboration is defined by the minimum delays required for a given output event with respect to an input event. This is a generalization of the semantics of UML Activities, where all input events are assumed to occur at the same time, and all output events occur at the same time. We give a semantic definition of the dynamic behavior of composed collaborations using the composition operators for control flow from UML Activity diagrams, in terms of partial order relationships among the involved input and output events. Based on these semantics, we provide formulas for calculating the performance of composed collaborations in terms of the performance of the sub-collaborations, where each delay is characterized by (a) a fixed value, (b) a range of values, and (c) a distribution (in the case of stochastic behaviours). We also propose approximations for the case of stochastic behavior with Normal distributions, and discuss the expected errors that may be introduced due to ignoring of shared resources or possible dependencies in the case of stochastic behaviours. A tool has been developed for evaluating the performance of complex collaborations, and examples and case studies are discussed to illustrate the applicability of the performance analysis and the visual notation which we introduced for representing the partial-order relationships of the input and output events.
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Modeling and Performance Analysis of Distributed Systems with Collaboration Behaviour DiagramsIsrar, Toqeer January 2014 (has links)
The use of distributed systems, involving multiple components, has become a common industry practice. However, modeling the behaviour of such systems is a challenge, especially when the behavior consists of several collaborations of different parties, each involving possibly several starting (input) and ending (output) events of the involved components. Furthermore, the global behavior should be described as a composition of several sub-behaviours, in the following called collaborations, and each collaboration may be further decomposed into several sub-collaborations. We assume that the performance of the elementary sub-collaborations is known, and that the performance of the global behavior should be determined from the performance of the contained elementary collaborations and the form of the composition.
A collaboration, in this thesis, is characterized by a partial order of input and output events, and the performance of the collaboration is defined by the minimum delays required for a given output event with respect to an input event. This is a generalization of the semantics of UML Activities, where all input events are assumed to occur at the same time, and all output events occur at the same time. We give a semantic definition of the dynamic behavior of composed collaborations using the composition operators for control flow from UML Activity diagrams, in terms of partial order relationships among the involved input and output events. Based on these semantics, we provide formulas for calculating the performance of composed collaborations in terms of the performance of the sub-collaborations, where each delay is characterized by (a) a fixed value, (b) a range of values, and (c) a distribution (in the case of stochastic behaviours). We also propose approximations for the case of stochastic behavior with Normal distributions, and discuss the expected errors that may be introduced due to ignoring of shared resources or possible dependencies in the case of stochastic behaviours. A tool has been developed for evaluating the performance of complex collaborations, and examples and case studies are discussed to illustrate the applicability of the performance analysis and the visual notation which we introduced for representing the partial-order relationships of the input and output events.
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Static Partial Order Reduction for Probabilistic Concurrent SystemsFernández-Díaz, Álvaro, Baier, Christel, Benac-Earle, Clara, Fredlund, Lars-Åke 10 September 2013 (has links) (PDF)
Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.
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Static Partial Order Reduction for Probabilistic Concurrent SystemsFernández-Díaz, Álvaro, Baier, Christel, Benac-Earle, Clara, Fredlund, Lars-Åke January 2012 (has links)
Sound criteria for partial order reduction for probabilistic concurrent systems have been presented in the literature. Their realization relies on a depth-first search-based approach for generating the reduced model. The drawback of this dynamic approach is that it can hardly be combined with other techniques to tackle the state explosion problem, e.g., symbolic probabilistic model checking with multi-terminal variants of binary decision diagrams. Following the approach presented by Kurshan et al. for non-probabilistic systems, we study partial order reduction techniques for probabilistic concurrent systems that can be realized by a static analysis. The idea is to inject the reduction criteria into the control flow graphs of the processes of the system to be analyzed. We provide the theoretical foundations of static partial order reduction for probabilistic concurrent systems and present algorithms to realize them. Finally, we report on some experimental results.
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