Tree-adjoining grammar

About: Tree-adjoining grammar is a research topic. Over the lifetime, 2491 publications have been published within this topic receiving 57813 citations.

Attribute Grammars and Mathematical Semantics

Abstract: Attribute grammars and mathematical semantics are rival language definition methods. We show that any attribute grammar G has a reformulation MS(G) within mathematical semantics. Most attribute grammars have properties that discipline the sets of equations the grammar gives to derivation trees. We list six such properties, and show that for a grammar G with one of these properties both MS(G) and the compiler for G can be simplified. Because these compiler-friendly properties are of independent interest, the paper is written in such a way that the first and last sections do not depend on the other sections.

MDL-Based Context-Free Graph Grammar Induction

Abstract: We present an algorithm for the inference of context-free graph grammars from examples. The algorithm builds on an earlier system for frequent substructure discovery, and is biased toward grammars that minimize description length. Grammar features include recursion, variables and relationships. We present an illustrative example, demonstrate the algorithm’s ability to learn in the presence of noise, and show real-world examples.

What's Decidable about Syntax-Guided Synthesis?

Abstract: Syntax-guided synthesis (SyGuS) is a recently proposed framework for program synthesis problems. The SyGuS problem is to find an expression or program generated by a given grammar that meets a correctness specification. Correctness specifications are given as formulas in suitable logical theories, typically amongst those studied in satisfiability modulo theories (SMT). In this work, we analyze the decidability of the SyGuS problem for different classes of grammars and correctness specifications. We prove that the SyGuS problem is undecidable for the theory of equality with uninterpreted functions (EUF).We identify a fragment of EUF, which we call regular-EUF, for which the SyGuS problem is decidable. We prove that this restricted problem is EXPTIME-complete and that the sets of solution expressions are precisely the regular tree languages. For theories that admit a unique, finite domain, we give a general algorithm to solve the SyGuS problem on tree grammars. Finite-domain theories include the bit-vector theory without concatenation. We prove SyGuS undecidable for a very simple bit-vector theory with concatenation, both for context-free grammars and for tree grammars. Finally, we give some additional results for linear arithmetic and bit-vector arithmetic along with a discussion of the implication of these results.

Well-Founded semantics for boolean grammars

Abstract: Boolean grammars [A. Okhotin, Information and Computation 194 (2004) 19-48] are a promising extension of context-free grammars that supports conjunction and negation. In this paper we give a novel semantics for boolean grammars which applies to all such grammars, independently of their syntax. The key idea of our proposal comes from the area of negation in logic programming, and in particular from the so-called well-founded semantics which is widely accepted in this area to be the “correct” approach to negation. We show that for every boolean grammar there exists a distinguished (three-valued) language which is a model of the grammar and at the same time the least fixed point of an operator associated with the grammar. Every boolean grammar can be transformed into an equivalent (under the new semantics) grammar in normal form. Based on this normal form, we propose an ${\mathcal{O}(n^3)}$ algorithm for parsing that applies to any such normalized boolean grammar. In summary, the main contribution of this paper is to provide a semantics which applies to all boolean grammars while at the same time retaining the complexity of parsing associated with this type of grammars.