Related papers: Ogden's Lemma for Regular Tree Languages
Solving of regular equations via Arden's Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that…
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical…
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…
This paper investigates a new property of formal languages called REG-measurability where REG is the class of regular languages. Intuitively, a language \(L\) is REG-measurable if there exists an infinite sequence of regular languages that…
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Tree-controlled grammars are context-free grammars where the derivation process is controlled in such a way that every word on a level of the derivation tree must belong to a certain control language. We investigate the generative capacity…
A substantial thread of recent work on latent tree learning has attempted to develop neural network models with parse-valued latent variables and train them on non-parsing tasks, in the hope of having them discover interpretable tree…
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 apply decision tree induction to the problem of discourse clue word sense disambiguation with a genetic algorithm. The automatic partitioning of the training set which is intrinsic to decision tree induction gives rise to linguistically…
Language models (LLMs) offer potential as a source of knowledge for agents that need to acquire new task competencies within a performance environment. We describe efforts toward a novel agent capability that can construct cues (or…
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.
Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language…
The HOM-problem, which asks whether the image of a regular tree language under a tree homomorphism is again regular, is known to be decidable. Since then, weighted versions of this problem for different semirings have also been…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
We study the portraits of isometries of rooted trees - the labelling of the tree, at each vertex, by the permutation of its descendants - in terms of languages. We characterize regularly branched self-similar groups in terms of…
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…
In this paper we introduce Latent Tree Language Model (LTLM), a novel approach to language modeling that encodes syntax and semantics of a given sentence as a tree of word roles. The learning phase iteratively updates the trees by moving…