Topic
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.
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05 Mar 1990
TL;DR: In this paper, the authors investigate the relationship between the algebraic definition of graph grammars and logic programming, and show that the operational semantics of any logic program can be faithfully simulated by a particular context-free hypergraph grammar.
Abstract: In this paper we investigate the relationship between the algebraic definition of graph grammars and logic programming. In particular, we show that the operational semantics of any logic program can be faithfully simulated by a particular context-free hypergraph grammar. In the process of doing that, we consider the issue of representing terms, formulas, and clauses as particular graphs or graph productions, by first evaluating the approaches already proposed for Term Rewriting Systems (TRS), and then by giving an original extension of those approaches, to be able to deal with the unique features of logic programming. Actually, not only does our representation of definite clauses by graph productions allow us to deal correctly with logical unification, but also it overcomes some of the problems encountered by other approaches for representing TRS's as graph grammars. The main result of the paper states the soundness and completeness of the representation of clauses by productions, and this correspondence is extended to entire computations, showing how a context-free grammar (over a suitable category of graphs) can be associated with a logic program. The converse holds as well, i.e. given any context-free graph grammar (over that category), a logic program can be extracted from it.
20 citations
TL;DR: This paper presents a natural generalization of the original Chomsky-Schutzenberger theorem to the tree languages of simple context-free tree grammars, using Rogers’s notion of multi-dimensional trees to state this latter theorem in a very general, abstract form.
Abstract: Weir [34] proved a Chomsky-Schutzenberger-like representation theorem for the string languages of tree-adjoining grammars, where the Dyck language Dn in the Chomsky-Schutzenberger characterization is replaced by the intersection D2n ∩ g(D2n), where g is a certain bijection on the alphabet consisting of 2n pairs of brackets. This paper presents a generalization of this theorem to the string languages that are the yield images of the tree languages generated by simple (i.e., linear and non-deleting) context-free tree grammars. This result is obtained through a natural generalization of the original Chomsky-Schutzenberger theorem to the tree languages of simple context-free tree grammars. We use Rogers’s [24,23] notion of multi-dimensional trees to state this latter theorem in a very general, abstract form.
20 citations
TL;DR: The parsing problem for permutations phrase grammars is considered, and it is shown how efficient linear-time parsing can be achieved for permutation phrase Grammars satisfying an extended notion of the LL(1) property.
Abstract: A permutation phrase is a grammatical phrase that specifies a syntactic construct as any permutation of a set of constituent elements. Permutation phrases allow for the concise and natural expression of free-order constructs as found in programming languages and notations such as C, Cobol, BibTEX, and Unix command lines.The conciseness and clarity of expression that permutation phrase grammars offer over context-free grammars are illustrated through a case study of the declarations in C. The parsing problem for permutation phrase grammars is considered, and it is shown how efficient linear-time parsing can be achieved for permutation phrase grammars satisfying an extended notion of the LL(1) property.
20 citations
TL;DR: Two results extending classical language properties into 2D are proved: non-recursive tile writing grammars (TRG) coincide with tiling systems (TS) and non-self-embedding TRG are suitably defined as corner Grammars, showing that they generate TS languages.
20 citations
TL;DR: It is proved that context-limited Grammars are equivalent to context-free grammars, the equivalence including ambiguity, and a new formal model for ambiguity, based on directed plane graphs with labeled edges, is outlined and compared with other models.
Abstract: A phrase structure grammar is called context-limited if there exists a partial ordering on its alphabet such that any letter on the left of any production is less than some letter on the right of the same production. It is proved that context-limited grammars are equivalent to context-free grammars, the equivalence including ambiguity. The notion of ambiguity in phrase structure grammars is discussed, and a new formal model for ambiguity, based on directed plane graphs with labeled edges, is outlined and compared with other models.
20 citations