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

Acquiring Word-Meaning Mappings for Natural Language Interfaces

This paper focuses on a system, WOLFIE (WOrd Learning From Interpreted Examples), that acquires a semantic lexicon from a corpus of sentences paired with semantic representations. The lexicon learned consists of phrases paired with meaning representations. WOLFIE is part of an integrated system that learns to transform sentences into representations such as logical database queries. Experimental results are presented demonstrating WOLFIE's ability to learn useful lexicons for a database interface in four different natural languages. The usefulness of the lexicons learned by WOLFIE are compared to those acquired by a similar system, with results favorable to WOLFIE. A second set of experiments demonstrates WOLFIE's ability to scale to larger and more difficult, albeit artificially generated, corpora. In natural language acquisition, it is difficult to gather the annotated data needed for supervised learning; however, unannotated data is fairly plentiful. Active learning methods attempt to select for annotation and training only the most informative examples, and therefore are potentially very useful in natural language applications. However, most results to date for active learning have only considered standard classification tasks. To reduce annotation effort while maintaining accuracy, we apply active learning to semantic lexicons. We show that active learning can significantly reduce the number of annotated examples required to achieve a given level of performance

Learning to Prove Safety over Parameterised Concurrent Systems (Full Version)

We revisit the classic problem of proving safety over parameterised concurrent systems, i.e., an infinite family of finite-state concurrent systems that are represented by some finite (symbolic) means. An example of such an infinite family is a dining philosopher protocol with any number n of processes (n being the parameter that defines the infinite family). Regular model checking is a well-known generic framework for modelling parameterised concurrent systems, where an infinite set of configurations (resp. transitions) is represented by a regular set (resp. regular transducer). Although verifying safety properties in the regular model checking framework is undecidable in general, many sophisticated semi-algorithms have been developed in the past fifteen years that can successfully prove safety in many practical instances. In this paper, we propose a simple solution to synthesise regular inductive invariants that makes use of Angluin's classic L* algorithm (and its variants). We provide a termination guarantee when the set of configurations reachable from a given set of initial configurations is regular. We have tested L* algorithm on standard (as well as new) examples in regular model checking including the dining philosopher protocol, the dining cryptographer protocol, and several mutual exclusion protocols (e.g. Bakery, Burns, Szymanski, and German). Our experiments show that, despite the simplicity of our solution, it can perform at least as well as existing semi-algorithms.Comment: Full version of FMCAD'17 pape

Zero-Shot Learning for Semantic Utterance Classification

We propose a novel zero-shot learning method for semantic utterance classification (SUC). It learns a classifier $f: X \to Y$ for problems where none of the semantic categories $Y$ are present in the training set. The framework uncovers the link between categories and utterances using a semantic space. We show that this semantic space can be learned by deep neural networks trained on large amounts of search engine query log data. More precisely, we propose a novel method that can learn discriminative semantic features without supervision. It uses the zero-shot learning framework to guide the learning of the semantic features. We demonstrate the effectiveness of the zero-shot semantic learning algorithm on the SUC dataset collected by (Tur, 2012). Furthermore, we achieve state-of-the-art results by combining the semantic features with a supervised method