Automated Software Debugging Using Hybrid Static/Dynamic Analysis

With the increasing complexity of today's software, the software development process is becoming highly time and resource consuming. The increasing number of software configurations, input parameters, usage scenarios, supporting platforms, external dependencies, and versions plays an important role in expanding the costs of maintaining and repairing unforeseeable software faults. To repair software faults, developers spend considerable time in identifying the scenarios leading to those faults and root-causing the problems. While software debugging remains largely manual, it is not the case with software testing and verification. The goal of this research is to improve the software development process in general, and software debugging process in particular, by devising techniques and methods for automated software debugging, which leverage the advances in automatic test case generation and replay. In this research, novel algorithms are devised to discover faulty execution paths in programs by utilizing already existing software test cases, which can be either automatically or manually generated. The execution traces, or alternatively, the sequence covers of the failing test cases are extracted. Afterwards, commonalities between these test case sequence covers are extracted, processed, analyzed, and then presented to the developers in the form of subsequences that may be causing the fault. The hypothesis is that code sequences that are shared between a number of faulty test cases for the same reason resemble the faulty execution path, and hence, the search space for the faulty execution path can be narrowed down by using a large number of test cases. To achieve this goal, an efficient algorithm is implemented for finding common subsequences among a set of code sequence covers. Optimization techniques are devised to generate shorter and more logical sequence covers, and to select subsequences with high likelihood of containing the root cause among the set of all possible common subsequences. A hybrid static/dynamic analysis approach is designed to trace back the common subsequences from the end to the root cause. A debugging tool is created to enable developers to use the approach, and integrate it with an existing Integrated Development Environment. The tool is also integrated with the environment's program editors so that developers can benefit from both the tool suggestions, and their source code counterparts. Finally, a comparison between the developed approach and the state-of-the-art techniques shows that developers need only to inspect a small number of lines in order to find the root cause of the fault. Furthermore, experimental evaluation shows that the algorithm optimizations lead to better results in terms of both the algorithm running time and the output subsequence length.

Multiscale Modeling and Simulation of Stepped Crystal Surfaces

A primary goal of this dissertation is to understand the links between mathematical models that describe crystal surfaces at three fundamental length scales: The scale of individual atoms, the scale of collections of atoms forming crystal defects, and macroscopic scale. Characterizing connections between different classes of models is a critical task for gaining insight into the physics they describe, a long-standing objective in applied analysis, and also highly relevant in engineering applications. The key concept I use in each problem addressed in this thesis is coarse graining, which is a strategy for connecting fine representations or models with coarser representations. Often this idea is invoked to reduce a large discrete system to an appropriate continuum description, e.g. individual particles are represented by a continuous density. While there is no general theory of coarse graining, one closely related mathematical approach is asymptotic analysis, i.e. the description of limiting behavior as some parameter becomes very large or very small. In the case of crystalline solids, it is natural to consider cases where the number of particles is large or where the lattice spacing is small. Limits such as these often make explicit the nature of links between models capturing different scales, and, once established, provide a means of improving our understanding, or the models themselves. Finding appropriate variables whose limits illustrate the important connections between models is no easy task, however. This is one area where computer simulation is extremely helpful, as it allows us to see the results of complex dynamics and gather clues regarding the roles of different physical quantities. On the other hand, connections between models enable the development of novel multiscale computational schemes, so understanding can assist computation and vice versa. Some of these ideas are demonstrated in this thesis. The important outcomes of this thesis include: (1) a systematic derivation of the step-flow model of Burton, Cabrera, and Frank, with corrections, from an atomistic solid-on-solid-type models in 1+1 dimensions; (2) the inclusion of an atomistically motivated transport mechanism in an island dynamics model allowing for a more detailed account of mound evolution; and (3) the development of a hybrid discrete-continuum scheme for simulating the relaxation of a faceted crystal mound. Central to all of these modeling and simulation efforts is the presence of steps composed of individual layers of atoms on vicinal crystal surfaces. Consequently, a recurring theme in this research is the observation that mesoscale defects play a crucial role in crystal morphological evolution.