Knowledge refinement tools seek to correct faulty rule-based systems by identifying and repairing faults indicated by training examples that provide evidence of faults. This thesis proposes mechanisms that improve the effectiveness and efficiency of refinement tools by the best use and selection of training examples. The refinement task is sufficiently complex that the space of possible refinements demands a heuristic search. Refinement tools typically use hill-climbing search to identify suitable repairs but run the risk of getting caught in local optima. A novel contribution of this thesis is solving the local optima problem by converting the hill-climbing search into a best-first search that can backtrack to previous refinement states. The thesis explores how different backtracking heuristics and training example ordering heuristics affect refinement effectiveness and efficiency. Refinement tools rely on a representative set of training examples to identify faults and influence repair choices. In real environments it is often difficult to obtain a large set of training examples, since each problem-solving task must be labelled with the expert's solution. Another novel aspect introduced in this thesis is informed selection of examples for knowledge refinement, where suitable examples are selected from a set of unlabelled examples, so that only the subset requires to be labelled. Conversely, if a large set of labelled examples is available, it still makes sense to have mechanisms that can select a representative set of examples beneficial for the refinement task, thereby avoiding unnecessary example processing costs. Finally, an experimental evaluation of example utilisation and selection strategies on two artificial domains and one real application are presented. Informed backtracking is able to effectively deal with local optima by moving search to more promising areas, while informed ordering of training examples reduces search effort by ensuring that more pressing faults are dealt with early on in the search. Additionally, example selection methods achieve similar refinement accuracy with significantly fewer examples.

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In a parallel vertex-centered finite element multigrid solver, segmental refinement can be used to avoid all inter-process communication on the fine grids. While domain decomposition methods generally require coupled subdomain processing for the numerical solution to a nonlinear elliptic boundary value problem, segmental refinement exploits that subdomains are almost decoupled with respect to high-frequency error components. This allows to perform multigrid with fully decoupled subdomains on the fine grids, which was proposed as a sequential low-storage algorithm by Brandt in the 1970s, and as a parallel algorithm by Brandt and Diskin in 1994. Adams published the first numerical results from a multilevel segmental refinement solver in 2014, confirming the asymptotic exactness of the scheme for a cell-centered finite volume implementation. We continue Brandt’s and Adams’ research by experimentally investigating the scheme’s accuracy with a vertex-centered finite element segmental refinement solver. We confirm that full multigrid accuracy can be preserved for a few segmental refinement levels, although we observe a different dependency on the segmental refinement parameter space. We show that various strategies for the grid transfers between the finest conventional multigrid level and the segmental refinement subdomains affect the solver accuracy. Scaling results are reported for a Cray XC30 with up to 4096 cores.

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Concurrent data structures have found increasingly widespread use in both multicore and distributed computing environments, thereby escalating the priority for verifying their correctness. The thread safe behavior of these concurrent objects is often described using formal semantics known as linearizability, which requires that  every operation in a concurrent object appears to take effect between its invocation and response. Quasi linearizability is a quantitative relaxation of linearizability to allow more implementation freedom for performance optimization.  However, ensuring the quantitative aspects of this new correctness condition is an arduous task. We propose the first method for formally verifying quasi linearizability of the implementation model of a concurrent data structure. The method is based on checking the refinement relation between the implementation model and a specification model via explicit state model checking. It can directly handle multi-threaded programs where each thread can make infinitely many method calls, without requiring the user to manually annotate for the linearization points. We have implemented and evaluated our method in the PAT model checking toolkit.  Our experiments show that the method is effective in verifying quasi linearizability and in detecting its violations. / Master of Science

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xvi, 145 p. : ill. (some col.) / The structures of several compounds in the [(PbSe)0.99]m[WSe2]n, [(PbSe)1.00]1[MoSe2]1, and [(SnSe)1.03]1[MoSe2]1 systems were determined using x-ray data. The structural determination using Rietveld methods was complicated by the strong preferred orientation of the samples, which resulted in x-ray diffraction scans with either 00l or hk0 reflections depending on the orientation of the sample in the diffractometer. Rietveld refinements of the [(PbSe)0.99]1[WSe2]1, [(PbSe)1.00]1[MoSe2]1, and [(SnSe)1.03]1[MoSe2]1 samples were compared to single crystal sample refinement results for [(MX)1+d]1[TX2]1, where M is a metal, T is a transition, X is a chalcogen, and d is the misfit parameter. The structural refinement yielded rock salt layer puckering values of 25 pm, 23 pm, and 36 pm for [(PbSe)0.99]1[WSe2]1, [(PbSe)1.00]1[MoSe2]1, and [(SnSe)1.03]1[MoSe2]1, respectively, which are all within the established literature range of 20 pm to 60 pm. The refinement of the hk0 reflections confirmed that the in plane structures were consistent with the dichalcogenide (P63mmc) and rock salt (Fm3m) structure types. Structures for the [(PbSe)0.99]m[WSe2]m isomer series where m = 1 to 5 were determined, and a systematic trend in structure as a function of the thickness of the constituent layers was discovered. The structure of the rock salt constituent was found to distort into pairs, forming alternating long and short distances along the c axis. This distortion decreases as the number of rock salt planes increases from 4 to 6 to 8 and is either absent or nearly so in compounds with a larger number of rock salt planes. The puckering distortion at the interface between the rock salt and the dichalcogenide is also observed in the inner rock salt layers but decreases in magnitude moving away from the rock salt – dichalcogenide interface. Structures of [(PbSe)0.99]m[WSe2]n where m = 1 or 2 and n = 1 or 2 were also determined. The degree of structural distortion is a function of the ratio of rock salt to dichalcogenide layers. This dissertation includes unpublished co-authored material. / Committee in charge: Dr. Thomas R. Dyke, Ph.D., Chairperson; Dr. David C. Johnson, Ph.D., Advisor; Dr. Catherine J. Page, Ph.D., Member; Dr. Andrew H. Marcus, Ph.D., Member; Dr. John L. Hardwick, Ph.D., Member; Dr. Richard Taylor, Ph.D., Outside Member

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