Grammars with two-sided contexts

In a recent paper (M. Barash, A. Okhotin, "Defining contexts in context-free grammars", LATA 2012), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the substring being defined. This paper proposes a more general model, in which context specifications may be two-sided, that is, both the left and the right contexts can be specified by the corresponding operators. The paper gives the definitions and establishes the basic theory of such grammars, leading to a normal form and a parsing algorithm working in time O(n^4), where n is the length of the input string.Comment: In Proceedings AFL 2014, arXiv:1405.527

A Simple Uniform Semantics for Concatenation-based Grammar

We define a more formal version of literal movement grammar (LMG) as outlined in [Gro95c], in such a way that it provides a simple framework that incorporates a large family of grammar formalisms (Head Grammar [Pol84], LCFRS, [Wei88]), PMCFG, [KNSK92] and String Attributed Grammars [Eng86]). The semantics is (both in rewriting and least fixed point definitions) simple and elegant, and sheds some new light on shared properties of the mentioned formalisms. We then define a restricted version called simple LMG and show that it generates languages that are not mildly context sensitive, yet preserves the polynomial time recognition property of LCFRS

Mild context-sensitivity and tuple-based generalizations of context-free grammar

This paper classifies a family of grammar formalisms that extend context-free grammar by talking about tuples of terminal strings, rather than independently combining single terminal words into larger single phrases. These include a number of well-known formalisms, such as head grammar and linear context-free rewriting systems, but also a new formalism, (simple) literal movement grammar, which strictly extends the previously known formalisms, while preserving polynomial time recognizability. The descriptive capacity of simple literal movement grammars is illustrated both formally through a weak generative capacity argument and in a more practical sense by the description of conjunctive cross-serial relative clauses in Dutch. After sketching a complexity result and drawing a number of conclusions from the illustrations, it is then suggested that the notion of mild context-sensitivity currently in use, that depends on the rather loosely defined concept of constant growth, needs a modification to apply sensibly to the illustrated facts; an attempt at such a revision is proposed

On TAG and Multicomponent TAG Parsing

The notion of mild context-sensitivity is an attempt to express the formal power needed to define the syntax of natural languages. However, all incarnati- ons of mildly context-sensitive formalisms are not equivalent. On the one hand, near the bottom of the hierarchy, we find tree adjoining grammars and, on the other hand, near the top of the hierarchy, we find multicomponent tree adjoining grammars. This paper proposes a polynomial parse time method for these two tree rewriting formalisms. This method uses range concatenation grammars as a high-level intermediate definition formalism, and yields several algorithms. Range concatenation grammar is a syntactic formalism which is both powerful, in so far as it extends linear context-free rewriting systems, and efficient, in so far as its sentences can be parsed in polynomial time. We show that any unrestricted tree adjoining grammar can be transformed into an equivalent range concatenation grammar which can be parsed in O(n6) time, and, moreover, if the input tree adjoining grammar has some restricted form, its parse time decreases to O(n5). We generalize one of these algorithms in order to process multicomponent tree adjoining grammars. We show some upper bounds on their parse times, and we introduce a hierarchy of restricted forms which can be parsed more efficiently. Our approach aims at giving both a new insight into the multicomponent adjunction mechanism and at providing a practical implementation scheme