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.

Symbol-Relation Grammars

Abstract: A common approach to the formal description of pictorial and visual languages makes use of formal grammars and rewriting mechanisms. The present paper is concerned with the formalism of Symbol?Relation Grammars (SR grammars, for short). Each sentence in an SR language is composed of a set of symbol occurrences representing visual elementary objects, which are related through a set of binary relational items. The main feature of SR grammars is the uniform way they use context-free productions to rewrite symbol occurrences as well as relation items. The clearness and uniformity of the derivation process for SR grammars allow the extension of well-established techniques of syntactic and semantic analysis to the case of SR grammars. The paper provides an accurate analysis of the derivation mechanism and the expressive power of the SR formalism. This is necessary to fully exploit the capabilities of the model. The most meaningful features of SR grammars as well as their generative power are compared with those of well-known graph grammar families. In spite of their structural simplicity, variations of SR grammars have a generative power comparable with that of expressive classes of graph grammars, such as the edNCE and the N-edNCE classes.

Tree-Adjoining Grammars as Abstract Categorial Grammars.

Abstract: categorial grammars are not intended as yet another grammatical formalism that would compete with other established formalisms. It should rather be seen as the kernel of a grammatical framework — in the spirit of (Ranta, 2002) — in which other existing grammatical models may be encoded. This paper illustrates this fact by showing how tree-adjoining grammars (Joshi and Schabes, 1997) may be embedded in abstract categorial grammars. This embedding exemplifies several features of the ACG framework: • The fact that the basic objects manipulated by an ACG are λ-terms allows higher-order operations to be defined. Typically, tree-adjunction is such a higher-order operation (Abrusci, Fouquere and Vauzeilles, 1999; Joshi and Kulick, 1997; Monnich, 1997). • The flexibility of the framework allows the embedding to be defined in two stages. A first ACG allows the tree langage of a given TAG to be generated. The abstract language of this first ACG corresponds to the derivation trees of the TAG. Then, a second ACG allows the corresponding string language to be extracted. The abstract language of this second ACG corresponds to the object language of the first one. 2. Abstract Categorial Grammars This section defines our notion of an abstract categorial grammar. We first introduce the notions of linear implicative types, higher-order linear signature, linear λ-terms built upon a higher-order linear signature, and lexicon. Let A be a set of atomic types. The set T (A) of linear implicative types built upon A is inductively defined as follows: 1. if a ∈ A, then a ∈ T (A); 2. if α, β ∈ T (A), then (α−◦ β) ∈ T (A). A higher-order linear signature consists of a triple Σ = 〈A,C, τ〉, where: 1. A is a finite set of atomic types; c © 2002 Philippe de Groote. Proceedings of the Sixth International Workshop on Tree Adjoining Grammar and Related Frameworks (TAG+6), pp. 101–106. Universita di Venezia. 102 Proceedings of TAG+6 2. C is a finite set of constants; 3. τ : C → T (A) is a function that assigns to each constant in C a linear implicative type in T (A). Let X be a infinite countable set of λ-variables. The set Λ(Σ) of linear λ-terms built upon a higher-order linear signature Σ = 〈A,C, τ〉 is inductively defined as follows: 1. if c ∈ C, then c ∈ Λ(Σ); 2. if x ∈ X , then x ∈ Λ(Σ); 3. if x ∈ X , t ∈ Λ(Σ), and x occurs free in t exactly once, then (λx. t) ∈ Λ(Σ); 4. if t, u ∈ Λ(Σ), and the sets of free variables of t and u are disjoint, then (t u) ∈ Λ(Σ). Λ(Σ) is provided with the usual notion of capture avoiding substitution, α-conversion, and β-reduction (Barendregt, 1984). Given a higher-order linear signature Σ = 〈A,C, τ〉, each linear λ-term in Λ(Σ) may be assigned a linear implicative type in T (A). This type assignment obeys an inference system whose judgements are sequents of the following form: Γ −Σ t : α where: 1. Γ is a finite set of λ-variable typing declarations of the form ‘x : β’ (with x ∈ X and β ∈ T (A)), such that any λ-variable is declared at most once; 2. t ∈ Λ(Σ); 3. α ∈ T (A). The axioms and inference rules are the following:

On the equivalence and containment problems for unambiguous regular expressions, grammars, and automata

Abstract: The known proofs that the equivalence and containment problems for the regular and for the linear context-free grammars are PSPACE-complete and undecidable, respecitvely, depend upon consideration of ambiguous grammars. We prove that this dependence is inherent. Deterministic polynomial time algorithms are presented for; (1) the equivalence and containment problems for the unambiguous regular grammars; (2) for all k ≥ 2, the equivalence and containment problems for the regular grammars of degree of ambiguity ≤ k; and (3) the problems of determining if an unambiguous linear context-free grammar is equivalent to or contains an arbitrary regular set. Simple extensions of the grammar classes in (1), (2), and (3) are shown to yield problems that are NP-hard or undecidable. Several new results on the relative economy of description of ambiguous versus unambiguous regular and linear contextfree grammars are also obtained. These results depend upon several observations on the solutions of systems of homogeneous linear difference equations and their relationship with the number of strings of a given length generated by an unambiguous regular or linear context-free grammar.

A graphical specification of model transformations with triple graph grammars

Abstract: Models and model transformations are the core concepts of OMG’s MDATM approach. Within this approach, most models are derived from the MOF and have a graph-based nature. In contrast, most of the current model transformations are specified textually. To enable a graphical specification of model transformation rules, this paper proposes to use triple graph grammars as declarative specification formalism. These triple graph grammars can be specified within the FUJABA tool and we argue that these rules can be more easily specified and they become more understandable and maintainable. To show the practicability of our approach, we present how to generate Tefkat rules from triple graph grammar rules, which helps to integrate triple graph grammars with a state of a art model transformation tool and shows the expressiveness of the concept.