Related papers: From indexed grammars to generating functions
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity.…
Grammar induction has made significant progress in recent years. However, it is not clear how the application of induced grammar could enhance practical performance in downstream tasks. In this work, we introduce an unsupervised grammar…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
The concept of context-free grammar in Combinatorics was first introduced by Chen in 1993. In 1996, Dumont significantly extended the theory of context-free grammars to a variety of other combinatorial models. Substantial progress in this…
We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite…
We implement a divide-and-concur iterative projection approach to context-free grammar inference. Unlike most state-of-the-art models of natural language processing, our method requires a relatively small number of discrete parameters,…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
We consider the cyclic closure of a language, and its generalisation to the operators $C^k$ introduced by Brandst\"adt. We prove that the cyclic closure of an indexed language is indexed, and that if $L$ is a context-free language then…
This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…
Conversational question answering systems often rely on semantic parsing to enable interactive information retrieval, which involves the generation of structured database queries from a natural language input. For information-seeking…
In this paper, we prove decidability properties and new results on the position of the family of languages generated by (circular) splicing systems within the Chomsky hierarchy. The two main results of the paper are the following. First, we…
We consider languages generated by weighted context-free grammars. It is shown that the behaviour of large texts is controlled by saddle-point equations for an appropriate generating function. We then consider ensembles of grammars, in…
We consider languages defined by signed grammars which are similar to context-free grammars except productions with signs associated to them are allowed. As a consequence, the words generated also have signs. We use the structure of the…
We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
We present a method for generating random hypergraphs in context-free hypergraph languages. It is obtained by adapting Mairson's generation algorithm for context-free string grammars to the setting of hyperedge replacement grammars. Our…
Constraint-based grammars can, in principle, serve as the major linguistic knowledge source for both parsing and generation. Surface generation starts from input semantics representations that may vary across grammars. For many declarative…
Large Language Models (LLMs), despite achieving state-of-the-art results in a number of evaluation tasks, struggle to maintain their performance when logical reasoning is strictly required to correctly infer a prediction. In this work, we…
We construct finitely generated simple algebras with prescribed growth types, which can be arbitrarily taken from a large variety of (super-polynomial) growth types. This (partially) answers a question raised by the author in a recent…
In this paper we use a contour integral method to derive a generating function in the form of a double series involving the product of two Chebyshev polynomials over generalized independent indices expressed in terms of the incomplete gamma…