Liao Zhang

Liao Zhang, David M. Cerna, Cezary Kaliszyk

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent proof step, and reasoning about it, given the multitude of possibilities, remains a daunting task for novice users. To improve the situation, several investigations have developed machine learning based guidance for tactic selection. Such approaches struggle to learn non-trivial relationships between the chosen tactic and the structure of the proof state and represent them as symbolic expressions. To address these issues we (i) We represent the problem as an Inductive Logic Programming (ILP) task, (ii) Using the ILP representation we enriched the feature space by encoding additional, computationally expensive properties as background knowledge predicates, (iii) We use this enriched feature space to learn rules explaining when a tactic is applicable to a given proof state, (iv) we use the learned rules to filter the output of an existing tactic selection approach and empirically show improvement over the non-filtering approaches.

Liao Zhang, Lasse Blaauwbroek, Bartosz Piotrowski et al.

We present a comparison of several online machine learning techniques for tactical learning and proving in the Coq proof assistant. This work builds on top of Tactician, a plugin for Coq that learns from proofs written by the user to synthesize new proofs. Learning happens in an online manner, meaning that Tactician's machine learning model is updated immediately every time the user performs a step in an interactive proof. This has important advantages compared to the more studied offline learning systems: (1) it provides the user with a seamless, interactive experience with Tactician and, (2) it takes advantage of locality of proof similarity, which means that proofs similar to the current proof are likely to be found close by. We implement two online methods, namely approximate k-nearest neighbors based on locality sensitive hashing forests and random decision forests. Additionally, we conduct experiments with gradient boosted trees in an offline setting using XGBoost. We compare the relative performance of Tactician using these three learning methods on Coq's standard library.

Liao Zhang

The security of industrial network has become an increasing concern in industry infrastructure operation. Motivated by on-going collaborations with Fortinet Corp., a security company, this project implements a testbed for supervisory control and data acquisition (SCADA) network security research by software emulation. Concepts about SCADA and Modbus protocol are reviewed in the report. Besides Modbus, vulnerabilities about several other industrial protocols are also studied for this project. In this report, a typical tank system following Modbus protocol is built as a testbed. Both attack and defense toolkits are introduced to emulate the attack and protection of the Modbus network. The emulation platform is also capable of entrapping hackers and gathering their activity data.