Patrick Young

Adrianna Gillman, Patrick Young, Per-Gunnar Martinsson

An algorithm for the direct inversion of the linear systems arising from Nystrom discretization of integral equations on one-dimensional domains is described. The method typically has O(N) complexity when applied to boundary integral equations (BIEs) in the plane with non-oscillatory kernels such as those associated with the Laplace and Stokes' equations. The scaling coefficient suppressed by the "big-O" notation depends logarithmically on the requested accuracy. The method can also be applied to BIEs with oscillatory kernels such as those associated with the Helmholtz and Maxwell equations; it is efficient at long and intermediate wave-lengths, but will eventually become prohibitively slow as the wave-length decreases. To achieve linear complexity, rank deficiencies in the off-diagonal blocks of the coefficient matrix are exploited. The technique is conceptually related to the H and H^2 matrix arithmetic of Hackbusch and co-workers, and is closely related to previous work on Hierarchically Semi-Separable matrices.

Fei Zuo, Xiaopeng Li, Patrick Young et al.

Binary code analysis allows analyzing binary code without having access to the corresponding source code. A binary, after disassembly, is expressed in an assembly language. This inspires us to approach binary analysis by leveraging ideas and techniques from Natural Language Processing (NLP), a rich area focused on processing text of various natural languages. We notice that binary code analysis and NLP share a lot of analogical topics, such as semantics extraction, summarization, and classification. This work utilizes these ideas to address two important code similarity comparison problems. (I) Given a pair of basic blocks for different instruction set architectures (ISAs), determining whether their semantics is similar or not; and (II) given a piece of code of interest, determining if it is contained in another piece of assembly code for a different ISA. The solutions to these two problems have many applications, such as cross-architecture vulnerability discovery and code plagiarism detection. We implement a prototype system INNEREYE and perform a comprehensive evaluation. A comparison between our approach and existing approaches to Problem I shows that our system outperforms them in terms of accuracy, efficiency and scalability. And the case studies utilizing the system demonstrate that our solution to Problem II is effective. Moreover, this research showcases how to apply ideas and techniques from NLP to large-scale binary code analysis.