Title: Symbolic Model Learning
Description: In this thesis, we study algorithms which can be used to extract, or learn, formal mathematical models from software systems and then using these models to test whether the given software systems satisfy certain security properties such as robustness against code injection attacks. Specifically, we focus on studying learning algorithms for automata and transducers and the symbolic extensions of these models, namely symbolic finite automata (SFAs). In a high level, this thesis contributes the following results: 1. In the first part of the thesis, we present a unified treatment of many common variations of the seminal L* algorithm for learning deterministic finite automata (DFAs) as a congruence learning algorithm for the underlying Nerode congruence which forms the basis of automata theory. Under this formulation the basic data structures used by different variations are unified as different ways to implement the Nerode congruence using queries. 2. Next, building on the new formulation of L*-style algorithms we proceed to develop new algorithms for learning transducer models.

Firstly, we present the first algorithm for learning deterministic partial transducers. Furthermore, we extend my algorithm into non-deterministic models by introducing a novel, generalized congruence relation over string transformations which is able to capture a subclass of string transformations with regular lookahead. We demonstrate that this class is able to capture many practical string transformation from the domain of string sanitizers in Web applications. 3. Classical learning algorithms for automata and transducers operate over finite alphabets and have a query complexity that scales linearly with the size of the alphabet. However, in practice, this dependence on the alphabet size hinders the performance of the algorithms. To address this issue, we develop the MAT* algorithm for learning symbolic finite state automata (SFAs) which operate over infinite alphabets. In practice, the MAT* learning algorithm allow us to plug custom transition learning algorithms which will efficiently infer the predicates in the transitions of the SFA without querying the whole alphabet set. 4.

Finally, we use our learning algorithm toolbox as the basis for the development of a set of black-box testing algorithms. More specifically, we present Grammar Oriented Filter Auditing (GOFA), a novel technique which allows one to utilize my learning algorithms to evaluate the robustness of a string sanitizer or filter against a set of attack strings given as a context-free grammar. Furthermore, because such grammars are many times unavailable, we developed sfadiff a differential testing technique based on symbolic automata learning which can be used in order to perform differential testing of two different parser implementations using SFA learning algorithms and we demonstrate how our algorithm can be used to develop program fingerprints. We evaluate our algorithms against state-of-the-art Web Application Firewalls and discover over 15 previously unknown vulnerabilities which result in evading the firewalls and performing code injection attacks in the backend Web application. Finally, we show how our learning algorithms can uncover vulnerabilities which are missed by other black-box methods such as fuzzing and grammar-based testing.