On the dynamics of a family of renormalization transformations

We study the family of renormalization transformations of the generalized $d$--dimensional diamond hierarchical Potts model in statistical mechanic and prove that their Julia sets and non-escaping loci are always connected, where $d\geq 2$. In particular, we prove that their Julia sets can never be a Sierpi\'{n}ski carpet if the parameter is real. We show that the Julia set is a quasicircle if and only if the parameter lies in the unbounded capture domain of these models. Moreover, the asymptotic formula of the Hausdorff dimension of the Julia set is calculated as the parameter tends to infinity.Comment: 21 pages, 5 figures, to appear in J. Math. Anal. App

Neural Machine Translation Inspired Binary Code Similarity Comparison beyond Function Pairs

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.Comment: Accepted by Network and Distributed Systems Security (NDSS) Symposium 201