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.

Regular grammars with truth values in lattice-ordered monoid and their languages

Abstract: In this study, we introduce the concept of lattice-valued regular grammars. Such grammars have become a necessary tool for the analysis of fuzzy finite automata. The relationship between lattice-valued finite automata (LA) and lattice-valued regular grammars (LRG) are discussed and we get the following results, for a given LRG, there exists an LA such that they accept the same languages, and vice versa. We also show the equivalence between deterministic lattice-valued regular grammars and deterministic lattice-valued finite automata.

Describing distributed systems by categorical graph grammars

Abstract: The structure of an asynchronous system of processes is described by a labeled hypergraph. It represents both the past and the present of the system. The set of all possible traces is defined by a hypergraph grammar. In the graph, actions and process states are represented by hyperedges. Each hyperedge is connected to some event nodes, some of which are considered to be predecessors of the edge, whereas others are successor nodes. This induces a partial ordering of the hyperedges. Some aspects of the Ada rendezvous are used as an example and translated into hypergraph productions.

Compact non-left-recursive grammars using the selective left-corner transform and factoring

Abstract: The left-corner transform removes left-recursion from (probabilistic) context-free grammars and unification grammars, permitting simple top-down parsing techniques to be used. Unfortunately the grammars produced by the standard left-corner transform are usually much larger than the original. The selective left-corner transform described in this paper produces a transformed grammar which simulates left-corner recognition of a user-specified set of the original productions, and top-down recognition of the others. Combined with two factorizations, it produces non-left-recursive grammars that are not much larger than the original.

On the syntactic structures of unrestricted grammars I. Generative grammars and phrase structure grammars

Abstract: Formal definitions for the syntactic structures of unrestricted grammars are given. The traditional forms for grammar productions give rise to “generative grammars” with “derivation structures” (where productions have the form α → β), and “phrase structure grammars” with “phrase structures” (where productions have the form A → B/μ-ν), two distinct notions of grammar and syntactic structure which become indistinguishable in the context free case, where the structures are trees. Parallel theories are developed for both kinds of grammar and structure. We formalize the notion of structural equivalence for derivations, extended to unrestricted grammars, and we prove that two derivations are structurally equivalent if and only if they have the same syntactic structure. Structural equivalence is an equivalence relation over the derivations of a grammar, and we give a simpler proof of a theorem by Griffiths that each equivalence class contains a rightmost derivation. We also give a proof for the uniqueness of the rightmost derivation, following a study of some of the properties of syntactic structures. Next, we investigate the relationship between derivation structures and phrase structures and show that the two concepts are nonisomorphic. There is a natural correspondence between generative productions and phrase structure productions, and, by extension, between the two kinds of grammars and between their derivations. But we show that the correspondence does not necessarily preserve structural equivalence, in either direction. However, if the correspondence from the productions of a phrase structure grammar to the productions of a generative grammar is a bijection, then structural equivalence on the generative derivations refines the image under the correspondence of structural equivalence on the phrase structure derivations.

From checking to inference via driving and dag grammars

Abstract: Abramov and Gluck have recently introduced a technique called URA for inverting first order functional programs. Given some desired output value, URA computes a potentially infinite sequence of substitutions/restrictions corresponding to the relevant input values. In some cases this process does not terminate.In the present paper, we propose a new program analysis for inverting programs. The technique works by computing a finite grammar describing the set of all input that relate to a given output. During the production of the grammar, the original program is implicitly transformed using so-called driving steps. Whereas URA is sound and complete, but sometimes fails to terminate, our technique always terminates and is complete, but not sound. As an example, we demonstrate how to derive type inference from type checking.The idea of approximating functional programs by grammars is not new. For instance, the second author has developed a technique using tree grammars to approximate termination behaviour of deforestation. However, for the present purposes it has been necessary to invent a new type of grammar that extends tree grammars by permitting a notion of sharing in the productions. These dag grammars seem to be of independent interest.