Related papers: From indexed grammars to generating functions
We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed in a very special case of complete free commutative Rota-Baxter algebras. This allows us to use free…
Computational argumentation has become an essential tool in various domains, including law, public policy, and artificial intelligence. It is an emerging research field in natural language processing that attracts increasing attention.…
We present two novel approaches to parsing context-free languages. The first approach is based on an extension of Brzozowski's derivative from regular expressions to context-free grammars. The second approach is based on a generalization of…
We explore the use of long-context capabilities in large language models to create synthetic reading comprehension data from entire books. Previous efforts to construct such datasets relied on crowd-sourcing, but the emergence of…
The word problem of a finitely generated group is the formal language of words over the generators which are equal to the identity in the group. If this language happens to be context-free, then the group is called context-free. Finitely…
Generating text from structured data is challenging because it requires bridging the gap between (i) structure and natural language (NL) and (ii) semantically underspecified input and fully specified NL output. Multilingual generation…
This paper addresses the uniform random generation of words from a context-free language (over an alphabet of size $k$), while constraining every letter to a targeted frequency of occurrence. Our approach consists in a multidimensional…
This work studies discrete diffusion probabilistic models with applications to natural language generation. We derive an alternative yet equivalent formulation of the sampling from discrete diffusion processes and leverage this insight to…
We study subsets $E$ of finitely generated groups where the set of all words over a given finite generating set that lie in $E$ forms a context-free language. We call these sets recognisably context-free. They are invariant of the choice of…
We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…
We investigate a multivariate growth series $\Gamma_L({\bf z}), {\bf z} \in \mathbb{C}^d$ associated with a regular language $L$ over an alphabet of cardinality $d.$ Our focus is on languages coming from subgroups of the free group and from…
The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D \cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is a local…
Many applications require categorization of text documents using predefined categories. The main approach to performing text categorization is learning from labeled examples. For many tasks, it may be difficult to find examples in one…
We present a formal framework for the development of a family of discriminative learning algorithms for Probabilistic Context-Free Grammars (PCFGs) based on a generalization of criterion-H. First of all, we propose the H-criterion as the…
There is a general phenomenon in algebra that numerous functors of homological significance admit characterization as derived limits of elementary functors defined over categories of free extensions. We demonstrate that upon restriction to…
Large Language Models offer new opportunities to devise automated implementation generation methods that can tackle problem solving activities beyond traditional methods, which require algorithmic specifications and can use only static…
Instruction-tuned large language models have shown remarkable performance in aligning generated text with user intentions across various tasks. However, maintaining human-like discourse structure in the generated text remains a challenging…
We study languages and formal power series associated to (variants of) Hammersley's process. We show that the ordinary Hammersley process yields a regular language and the Hammersley tree process yields deterministic context-free (but…
We propose a language-agnostic way of automatically generating sets of semantically similar clusters of entities along with sets of "outlier" elements, which may then be used to perform an intrinsic evaluation of word embeddings in the…
To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of…