Some Remarks on Deciding Equivalence for Graph-To-Graph Transducers

We study the following decision problem: given two mso transductions that input and output graphs of bounded treewidth, decide if they are equivalent, i.e. isomorphic inputs give isomorphic outputs. We do not know how to decide it, but we propose an approach that uses automata manipulating elements of a ring extended with division. The approach works for a variant of the problem, where isomorphism on output graphs is replaced by a relaxation of isomorphism

Decidability of Querying First-Order Theories via Countermodels of Finite Width

We propose a generic framework for establishing the decidability of a wide range of logical entailment problems (briefly called querying), based on the existence of countermodels that are structurally simple, gauged by certain types of width measures (with treewidth and cliquewidth as popular examples). As an important special case of our framework, we identify logics exhibiting width-finite finitely universal model sets, warranting decidable entailment for a wide range of homomorphism-closed queries, subsuming a diverse set of practically relevant query languages. As a particularly powerful width measure, we propose Blumensath's partitionwidth, which subsumes various other commonly considered width measures and exhibits highly favorable computational and structural properties. Focusing on the formalism of existential rules as a popular showcase, we explain how finite partitionwidth sets of rules subsume other known abstract decidable classes but -- leveraging existing notions of stratification -- also cover a wide range of new rulesets. We expose natural limitations for fitting the class of finite unification sets into our picture and provide several options for remedy

The category of MSO transductions

MSO transductions are binary relations between structures which are defined using monadic second-order logic. MSO transductions form a category, since they are closed under composition. We show that many notions from language theory, such as recognizability or tree decompositions, can be defined in an abstract way that only refers to MSO transductions and their compositions

Complexity and algorithms related to two classes of graph problems

This thesis addresses the problems associated with conversions on graphs and editing by removing a matching. We study the f-reversible processes, which are those associated with a threshold value for each vertex, and whose dynamics depends on the number of neighbors with different state for each vertex. We set a tight upper bound for the period and transient lengths, characterize all trees that reach the maximum transient length for 2-reversible processes, and we show that determining the size of a minimum conversion set is NP-hard. We show that the AND-OR model defines a convexity on graphs. We show results of NP-completeness and efficient algorithms for certain convexity parameters for this new one, as well as approximate algorithms. We introduce the concept of generalized threshold processes, where the results are NP-completeness and efficient algorithms for both non relaxed and relaxed versions. We study the problem of deciding whether a given graph admits a removal of a matching in order to destroy all cycles. We show that this problem is NP-hard even for subcubic graphs, but admits efficient solution for several graph classes. We study the problem of deciding whether a given graph admits a removal of a matching in order to destroy all odd cycles. We show that this problem is NP-hard even for planar graphs with bounded degree, but admits efficient solution for some graph classes. We also show parameterized results.Esta tese aborda problemas associados a conversões em grafos e de edição pela remoção de um emparelhamento. Estudamos processos f-reversíveis, que são aqueles associados a um valor de limiar para cada vértice e cuja dinâmica depende da quantidade de vizinhos com estado contrário para cada vértice. Estabelecemos um limite superior justo para o tamanho do período e transiente, caracterizamos todas as árvores que alcançam o transiente máximo em processos 2-reversíveis e mostramos que determinar o tamanho de um conjunto conversor mínimo é NP-difícil. Mostramos que o modelo AND-OR define uma convexidade sobre grafos. Mostramos resultados de NP-completude e algoritmos eficientes para certos parâmetros de convexidade para esta nova, assim como algoritmos aproximativos. Introduzimos o conceito de processos de limiar generalizados, onde mostramos resultados de NP-completude e algoritmos eficientes para ambas as versões não relaxada e relaxada. Estudamos o problema de decidir se um dado grafo admite uma remoção de um emparelhamento de modo a remover todos os ciclos. Mostramos que este problema é NP-difícil mesmo para grafos subcúbicos, mas admite solução eficiente para várias classes de grafos. Estudamos o problema de decidir se um dado grafo admite uma remoção de um emparelhamento de modo a remover todos os ciclos ímpares. Mostramos que este problema é NP-difícil mesmo para grafos planares com grau limitado, mas admite solução eficiente para algumas classes de grafos. Mostramos também resultados parametrizados

Constraint analysis for DSP code generation

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From surfaces to objects : Recognizing objects using surface information and object models.

This thesis describes research on recognizing partially obscured objects using surface information like Marr's 2D sketch ([MAR82]) and surface-based geometrical object models. The goal of the recognition process is to produce a fully instantiated object hypotheses, with either image evidence for each feature or explanations for their absence, in terms of self or external occlusion. The central point of the thesis is that using surface information should be an important part of the image understanding process. This is because surfaces are the features that directly link perception to the objects perceived (for normal "camera-like" sensing) and because surfaces make explicit information needed to understand and cope with some visual problems (e.g. obscured features). Further, because surfaces are both the data and model primitive, detailed recognition can be made both simpler and more complete. Recognition input is a surface image, which represents surface orientation and absolute depth. Segmentation criteria are proposed for forming surface patches with constant curvature character, based on surface shape discontinuities which become labeled segmentation- boundaries. Partially obscured object surfaces are reconstructed using stronger surface based constraints. Surfaces are grouped to form surface clusters, which are 3D identity-independent solids that often correspond to model primitives. These are used here as a context within which to select models and find all object features. True three-dimensional properties of image boundaries, surfaces and surface clusters are directly estimated using the surface data. Models are invoked using a network formulation, where individual nodes represent potential identities for image structures. The links between nodes are defined by generic and structural relationships. They define indirect evidence relationships for an identity. Direct evidence for the identities comes from the data properties. A plausibility computation is defined according to the constraints inherent in the evidence types. When a node acquires sufficient plausibility, the model is invoked for the corresponding image structure.Objects are primarily represented using a surface-based geometrical model. Assemblies are formed from subassemblies and surface primitives, which are defined using surface shape and boundaries. Variable affixments between assemblies allow flexibly connected objects. The initial object reference frame is estimated from model-data surface relationships, using correspondences suggested by invocation. With the reference frame, back-facing, tangential, partially self-obscured, totally self-obscured and fully visible image features are deduced. From these, the oriented model is used for finding evidence for missing visible model features. IT no evidence is found, the program attempts to find evidence to justify the features obscured by an unrelated object. Structured objects are constructed using a hierarchical synthesis process. Fully completed hypotheses are verified using both existence and identity constraints based on surface evidence. Each of these processes is defined by its computational constraints and are demonstrated on two test images. These test scenes are interesting because they contain partially and fully obscured object features, a variety of surface and solid types and flexibly connected objects. All modeled objects were fully identified and analyzed to the level represented in their models and were also acceptably spatially located. Portions of this work have been reported elsewhere ([FIS83], [FIS85a], [FIS85b], [FIS86]) by the author

Estudio de corpus de las oraciones de relativo en el inglés australiano de los siglos XVIII y XIX

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Filología, leída el 18-01-2022This study aims at analysing relative clauses in Australian English from 1788 to 1900 and the possible influence which 18th and 19th century grammarians had on the first settlers and, lately, on the Australian inhabitants. The main objective is to analyse the different relativization strategies, that is, case-marked wh- relatives, the invariable that,and the gap relativizer zero, and the effect of prescriptive grammars, which could be seen on the medium, written or oral, and the formality of the context. These two factors may result in the use of any of the strategies previously described either by following normative principles or by slowly distancing from such precepts, which might contribute to an endonormative innovation from a linguistic exonormative reality based on British English. Additionally, this investigation could determine to what extent the text category and the medium may affect the distribution of relatives, the syntactic functions which they realize, the placement of the preposition when complementing a preposition, and the typology, that is, restrictive or non-restrictive. In conclusion, this research will contribute to a detailed analysis which allows, on the one hand, to learn about some aspects of early Australian English and, on the other hand, a diachronic view of this specific variety or a future contrastive analysis with other varieties of English...El presente estudio se centra en las oraciones de relativo en el inglés australiano desde1788 a 1900 y la posible influencia de las gramáticas prescriptivas en los primeros pobladores y, posteriormente, en los habitantes de Australia. El principal objetivo es el análisis de las diferentes estrategias de relativización, a saber, los pronombres de relativo introducidos por wh, el invariable that y el relativo omitido zero, y la repercusión de las gramáticas prescriptivas del siglo XVIII, que podría verse reflejada, por un lado, en el medio, es decir, escrito o hablado, y por otro lado, en la formalidad del contexto. Estos dos factores podrían suponer el uso de cada una de las estrategias bien siguiendo las normas dictadas en las gramáticas o mostrando cierto distanciamiento de tales preceptos, que podría dar paso a su vez a una innovación endonormativa desde una realidad lingüística exonormativa basada en el inglés británico. Adicionalmente, este análisis puede determinar hasta qué punto la categoría textual y el medio pueden afectar a la distribución de los relativos, las funciones sintácticas que desempeñan, la colocación de la preposición en el caso de tratarse de un complemento de la misma y la tipología, es decir, si la oración es especificativa o explicativa. En definitiva, este estudio pretende contribuir a un análisis detallado que permitirá, por un lado, conocer la base lingüística del inglés australiano y, por otro, un estudio diacrónico de la propia variedad o un futuro análisis contrastivo con otras variantes del inglés...Fac. de FilologíaTRUEunpu