Efficient learning of context-free grammars from positive structural examples

AbstractIn this paper, we introduce a new normal form for context-free grammars, called reversible context-free grammars, for the problem of learning context-free grammars from positive-only examples. A context-free grammar G = (N, Σ, P, S) is said to be reversible if (1) A → α and B → α in P implies A = B and (2) A → αBβ and A → αCβ in P implies B = C. We show that the class of reversible context-free grammars can be identified in the limit from positive samples of structural descriptions and there exists an efficient algorithm to identify them from positive samples of structural descriptions, where a structural description of a context-free grammar is an unlabelled derivation tree of the grammar. This implies that if positive structural examples of a reversible context-free grammar for the target language are available to the learning algorithm, the full class of context-free languages can be learned efficiently from positive samples

Synthesizing Program Input Grammars

We present an algorithm for synthesizing a context-free grammar encoding the language of valid program inputs from a set of input examples and blackbox access to the program. Our algorithm addresses shortcomings of existing grammar inference algorithms, which both severely overgeneralize and are prohibitively slow. Our implementation, GLADE, leverages the grammar synthesized by our algorithm to fuzz test programs with structured inputs. We show that GLADE substantially increases the incremental coverage on valid inputs compared to two baseline fuzzers

Inducing Probabilistic Grammars by Bayesian Model Merging

We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or nonterminals) are {\em merged} to achieve generalization and a more compact representation. The choice of what to merge and when to stop is governed by the Bayesian posterior probability of the grammar given the data, which formalizes a trade-off between a close fit to the data and a default preference for simpler models (`Occam's Razor'). The general scheme is illustrated using three types of probabilistic grammars: Hidden Markov models, class-based $n$-grams, and stochastic context-free grammars.Comment: To appear in Grammatical Inference and Applications, Second International Colloquium on Grammatical Inference; Springer Verlag, 1994. 13 page

Wrapper Maintenance: A Machine Learning Approach

The proliferation of online information sources has led to an increased use of wrappers for extracting data from Web sources. While most of the previous research has focused on quick and efficient generation of wrappers, the development of tools for wrapper maintenance has received less attention. This is an important research problem because Web sources often change in ways that prevent the wrappers from extracting data correctly. We present an efficient algorithm that learns structural information about data from positive examples alone. We describe how this information can be used for two wrapper maintenance applications: wrapper verification and reinduction. The wrapper verification system detects when a wrapper is not extracting correct data, usually because the Web source has changed its format. The reinduction algorithm automatically recovers from changes in the Web source by identifying data on Web pages so that a new wrapper may be generated for this source. To validate our approach, we monitored 27 wrappers over a period of a year. The verification algorithm correctly discovered 35 of the 37 wrapper changes, and made 16 mistakes, resulting in precision of 0.73 and recall of 0.95. We validated the reinduction algorithm on ten Web sources. We were able to successfully reinduce the wrappers, obtaining precision and recall values of 0.90 and 0.80 on the data extraction task

Overfitting in Synthesis: Theory and Practice (Extended Version)

In syntax-guided synthesis (SyGuS), a synthesizer's goal is to automatically generate a program belonging to a grammar of possible implementations that meets a logical specification. We investigate a common limitation across state-of-the-art SyGuS tools that perform counterexample-guided inductive synthesis (CEGIS). We empirically observe that as the expressiveness of the provided grammar increases, the performance of these tools degrades significantly. We claim that this degradation is not only due to a larger search space, but also due to overfitting. We formally define this phenomenon and prove no-free-lunch theorems for SyGuS, which reveal a fundamental tradeoff between synthesizer performance and grammar expressiveness. A standard approach to mitigate overfitting in machine learning is to run multiple learners with varying expressiveness in parallel. We demonstrate that this insight can immediately benefit existing SyGuS tools. We also propose a novel single-threaded technique called hybrid enumeration that interleaves different grammars and outperforms the winner of the 2018 SyGuS competition (Inv track), solving more problems and achieving a $5\times$ mean speedup.Comment: 24 pages (5 pages of appendices), 7 figures, includes proofs of theorem