Related papers: An undecidable property of context-free languages

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…

For any context-free grammar, we build a transition diagram, that is, a finite directed graph with labeled arcs, which describes the work of the grammar. This approach is new, and it is different from previously known graph models. We…

In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb{Z}$ is interpretable by positive existential formulas in…

Despite large language models' (LLMs) recent advancements, their bias and hallucination issues persist, and their ability to offer consistent preferential rankings remains underexplored. This study investigates the capacity of LLMs to…

We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.

We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the…

It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of the full elementary theory of the finitely generated free…

Are large language models (LLMs) sensitive to the distinction between humanly possible and impossible languages? This question was recently used in a broader debate on whether LLMs and humans share the same innate learning biases. Previous…

We study a formalization of the grammar induction problem that models sentences as being generated by a compound probabilistic context-free grammar. In contrast to traditional formulations which learn a single stochastic grammar, our…

The present work analyzes the redundancy of sets of combinatorial objects produced by a weighted random generation algorithm proposed by Denise et al. This scheme associates weights to the terminals symbols of a weighted context-free…

We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega…

In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be…

This paper proposes decoupling the dependency tree from word order, such that surface ordering is not determined by traversing the dependency tree. We develop the notion of a \emph{word order domain structure}, which is linked but…

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the…

Kleinberg and Mullainathan showed that language generation in the limit is always possible at the level of computability: given enough positive examples, a learner can eventually generate data indistinguishable from a target language.…

In this note we provide a (decidable) graph-structural characterisation of the infiniteness of $L(w_1, ..., w_k)$, where $L(w_1, ..., w_k) = \{w \in A^* | |w|_{w_1} = \cdots = |w|_{w_k}\}$ is the set of all words that contain the same…

We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…

Nonsensical and anomalous sentences have been instrumental in the development of computational models of semantic interpretation. A core challenge is to distinguish between what is merely anomalous (but can be interpreted given a supporting…

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…

The ability to produce and understand an unlimited number of different sentences is a hallmark of human language. Linguists have sought to define the essence of this generative capacity using formal grammars that describe the syntactic…