Formal verification of higher-order probabilistic programs

Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru, derive their expressiveness from a powerful combination of continuous distributions, conditioning, and higher-order functions. Although very important for practical applications, these combined features raise fundamental challenges for program semantics and verification. Several recent works offer promising answers to these challenges, but their primary focus is on semantical issues. In this paper, we take a step further and we develop a set of program logics, named PPV, for proving properties of programs written in an expressive probabilistic higher-order language with continuous distributions and operators for conditioning distributions by real-valued functions. Pleasingly, our program logics retain the comfortable reasoning style of informal proofs thanks to carefully selected axiomatizations of key results from probability theory. The versatility of our logics is illustrated through the formal verification of several intricate examples from statistics, probabilistic inference, and machine learning. We further show the expressiveness of our logics by giving sound embeddings of existing logics. In particular, we do this in a parametric way by showing how the semantics idea of (unary and relational) TT-lifting can be internalized in our logics. The soundness of PPV follows by interpreting programs and assertions in quasi-Borel spaces (QBS), a recently proposed variant of Borel spaces with a good structure for interpreting higher order probabilistic programs

Perturbative Quantum Field Theory on Random Trees

In this paper we start a systematic study of quantum field theory on random trees. Using precise probability estimates on their Galton-Watson branches and a multiscale analysis, we establish the general power counting of averaged Feynman amplitudes and check that they behave indeed as living on an effective space of dimension 4/3, the spectral dimension of random trees. In the `just renormalizable' case we prove convergence of the averaged amplitude of any completely convergent graph, and establish the basic localization and subtraction estimates required for perturbative renormalization. Possible consequences for an SYK-like model on random trees are briefly discussed.Comment: 44 page

Understanding Android Obfuscation Techniques: A Large-Scale Investigation in the Wild

In this paper, we seek to better understand Android obfuscation and depict a holistic view of the usage of obfuscation through a large-scale investigation in the wild. In particular, we focus on four popular obfuscation approaches: identifier renaming, string encryption, Java reflection, and packing. To obtain the meaningful statistical results, we designed efficient and lightweight detection models for each obfuscation technique and applied them to our massive APK datasets (collected from Google Play, multiple third-party markets, and malware databases). We have learned several interesting facts from the result. For example, malware authors use string encryption more frequently, and more apps on third-party markets than Google Play are packed. We are also interested in the explanation of each finding. Therefore we carry out in-depth code analysis on some Android apps after sampling. We believe our study will help developers select the most suitable obfuscation approach, and in the meantime help researchers improve code analysis systems in the right direction

05451 Abstracts Collection -- Beyond Program Slicing

From 06.11.05 to 11.11.05, the Dagstuhl Seminar 05451 ``Beyond Program Slicing\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available