Slices are digraphs that can be composed together to form larger digraphs.In this thesis we introduce the foundations of a theory whose aim is to provide ways of defining and manipulating infinite families of combinatorial objects such as graphs, partial orders, logical equations etc. We give special attentionto objects that can be represented as sequences of slices. We have successfully applied our theory to obtain novel results in three fields: concurrency theory,combinatorics and logic. Some notable results are: Concurrency Theory: We prove that inclusion and emptiness of intersection of the causalbehavior of bounded Petri nets are decidable. These problems had been open for almost two decades. We introduce an algorithm to transitively reduce infinite familiesof DAGs. This algorithm allows us to operate with partial order languages defined via distinct formalisms, such as, Mazurkiewicztrace languages and message sequence chart languages. Combinatorics: For each constant z ∈ N, we define the notion of z-topological or-der for digraphs, and use it as a point of connection between the monadic second order logic of graphs and directed width measures, such as directed path-width and cycle-rank. Through this connection we establish the polynomial time solvability of a large numberof natural counting problems on digraphs admitting z-topological orderings. Logic: We introduce an ordered version of equational logic. We show thatthe validity problem for this logic is fixed parameter tractable withrespect to the depth of the proof DAG, and solvable in polynomial time with respect to several notions of width of the equations being proved. In this way we establish the polynomial time provability of equations that can be out of reach of techniques based on completion and heuristic search. / <p>QC 20131120</p>

Der Bezirk Xilingol wurde als geeignetes Beispiel ausgewählt, weil es zu einem großen Flächenanteil von Grassteppe bedeckt ist und fast alle Phasen der Umweltpolitik Chinas durchlaufen hat. Es wurden zwei deutlich voneinander abgrenzbare Phasen identifiziert, von 1975 bis 2000 und von 2000 bis 2015. Während der ersten Phase, bis 2000, war Landdegradation der dominante Landnutzungswandelprozess, der 11.4 % der Gesamtfläche betraf. In dieser Phase war die menschliche Einflussnahme der Hauptfaktor in acht Landkreisen, die sich ändernden Wasserverhältnisse war es in sechs Landkreisen. Während der zweiten Phase, ab 2000, setzte ein spürbare Erholung des Zustandes auf 12 % des Gesamtgebietes ein, während die Degradation jedoch weiter voranschritt und zusätzliche 9,5 % des Landes veränderte. Während dieser Phase wurde die Städtebildung zum dominanten Treiber für die Landdegradierung in sieben Landkreisen, während der Einfluss menschlicher Störungen und der Wasserverfügbarkeit wieder zurückging. Nach der Identifizierung der Haupttreiber für die Landdegradation, wurde die komplexe Beziehung zwischen verschiedenen Treibern und der Grassteppen-Degradation untersucht. Die Ergebnisse zeigten, dass die Beziehung zwischen dicht bedeckter, moderat bedeckter, und spärlich bedeckter Grassteppe und die Dichte des Schafbesatzes für die Degradationsdynamik in der Grassteppe verantwortlich waren. In dieser Arbeit wurden die Methoden der Clusteranalyse, der Partial-Order-Theorie, und der Hasse Diagramme eingesetzt, um die Haupttreiber der Landdegradation auf Landkreisebene zu identifizieren. Dann wurde ein Ansatz aus dem maschinellen Lernen, XGBoost (eXtreme Gradient Boosting) verwendet, um die Dynamik der Grassteppen-Degradation vorauszusagen. Darüber hinaus wurde SHAP (SHapley Additive exPlanations) eingesetzt, um das von XGBoost erstellte Black-Box-Modell zu in seine Bestanteile zu zerlegen und für jedes Degradations-Pixel in der Karte den Haupttreiber zu extrahieren. / The aims of this thesis are to gain an integrated and systematic understanding of the processes and determinants of land degradation on the Mongolian Plateau. Xilingol was chosen as a suitable example, mainly since it is covered by vast grassland, and has experienced almost all ecological policies that have been implemented in China. Two distinct phases were identified in this region: 1975-2000 and 2000-2015. During the first phase (up to 2000), land degradation was the dominant land use change process, accounting for 11.4% of the total area. During this phase, human disturbance was the major driver in eight counties, whereas the water condition was the dominant driver in six counties. During the second phase (post-2000), land restoration increased (12.0% of the total area), whereas degradation continued, resulting in a further 9.5% of degraded land. During this phase, urbanisation became the dominant driver of land degradation in seven counties, while effects resulting from human disturbance and water availability decreased after 2000. After identifying the major drivers of degradation, the complex relationships between drivers and grassland degradation were captured. The results indicated that the distance to dense, moderately dense grass and sparse grass and sheep density were responsible for the grassland degradation dynamics. In this thesis, a clustering method, partial order theory and Hasse diagram techniques were first used to identify the major drivers of land degradation at the county level. Subsequently, an approach from machine learning, XGBoost (eXtreme Gradient Boosting), was used to predict the dynamics of grassland degradation. Moreover, SHAP (SHapley Additive exPlanations) values were used to open up the black box model, and the primary driver was extracted for each pixel showing degradation.