A Theory of Formal Synthesis via Inductive Learning

Formal synthesis is the process of generating a program satisfying a high-level formal specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of methods that learn programs from examples as formal inductive synthesis. In this paper, we present a theoretical framework for formal inductive synthesis. We discuss how formal inductive synthesis differs from traditional machine learning. We then describe oracle-guided inductive synthesis (OGIS), a framework that captures a family of synthesizers that operate by iteratively querying an oracle. An instance of OGIS that has had much practical impact is counterexample-guided inductive synthesis (CEGIS). We present a theoretical characterization of CEGIS for learning any program that computes a recursive language. In particular, we analyze the relative power of CEGIS variants where the types of counterexamples generated by the oracle varies. We also consider the impact of bounded versus unbounded memory available to the learning algorithm. In the special case where the universe of candidate programs is finite, we relate the speed of convergence to the notion of teaching dimension studied in machine learning theory. Altogether, the results of the paper take a first step towards a theoretical foundation for the emerging field of formal inductive synthesis

Sciduction: Combining Induction, Deduction, and Structure for Verification and Synthesis

Even with impressive advances in automated formal methods, certain problems in system verification and synthesis remain challenging. Examples include the verification of quantitative properties of software involving constraints on timing and energy consumption, and the automatic synthesis of systems from specifications. The major challenges include environment modeling, incompleteness in specifications, and the complexity of underlying decision problems. This position paper proposes sciduction, an approach to tackle these challenges by integrating inductive inference, deductive reasoning, and structure hypotheses. Deductive reasoning, which leads from general rules or concepts to conclusions about specific problem instances, includes techniques such as logical inference and constraint solving. Inductive inference, which generalizes from specific instances to yield a concept, includes algorithmic learning from examples. Structure hypotheses are used to define the class of artifacts, such as invariants or program fragments, generated during verification or synthesis. Sciduction constrains inductive and deductive reasoning using structure hypotheses, and actively combines inductive and deductive reasoning: for instance, deductive techniques generate examples for learning, and inductive reasoning is used to guide the deductive engines. We illustrate this approach with three applications: (i) timing analysis of software; (ii) synthesis of loop-free programs, and (iii) controller synthesis for hybrid systems. Some future applications are also discussed

Weighted Automata Extraction from Recurrent Neural Networks via Regression on State Spaces

We present a method to extract a weighted finite automaton (WFA) from a recurrent neural network (RNN). Our algorithm is based on the WFA learning algorithm by Balle and Mohri, which is in turn an extension of Angluin's classic \lstar algorithm. Our technical novelty is in the use of \emph{regression} methods for the so-called equivalence queries, thus exploiting the internal state space of an RNN to prioritize counterexample candidates. This way we achieve a quantitative/weighted extension of the recent work by Weiss, Goldberg and Yahav that extracts DFAs. We experimentally evaluate the accuracy, expressivity and efficiency of the extracted WFAs.Comment: AAAI 2020. We are preparing to distribute the implementatio

Symbolic Model Learning: New Algorithms and Applications

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

Should We Learn Probabilistic Models for Model Checking? A New Approach and An Empirical Study

Many automated system analysis techniques (e.g., model checking, model-based testing) rely on first obtaining a model of the system under analysis. System modeling is often done manually, which is often considered as a hindrance to adopt model-based system analysis and development techniques. To overcome this problem, researchers have proposed to automatically "learn" models based on sample system executions and shown that the learned models can be useful sometimes. There are however many questions to be answered. For instance, how much shall we generalize from the observed samples and how fast would learning converge? Or, would the analysis result based on the learned model be more accurate than the estimation we could have obtained by sampling many system executions within the same amount of time? In this work, we investigate existing algorithms for learning probabilistic models for model checking, propose an evolution-based approach for better controlling the degree of generalization and conduct an empirical study in order to answer the questions. One of our findings is that the effectiveness of learning may sometimes be limited.Comment: 15 pages, plus 2 reference pages, accepted by FASE 2017 in ETAP