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Human language is known to exhibit a nested, hierarchical structure, allowing us to form complex sentences out of smaller pieces. However, many state-of-the-art neural networks models such as Transformers have no explicit hierarchical…

The notion of transducer integer sequences is considered through a series of examples. By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite automata encoding tree morphisms…

End-to-end approaches for sequence tasks are becoming increasingly popular. Yet for complex sequence tasks, like speech translation, systems that cascade several models trained on sub-tasks have shown to be superior, suggesting that the…

We first show that increasing trees are in bijection with set compositions, extending simultaneously a recent result on trees due to Tonks and a classical result on increasing binary trees. We then consider algebraic structures on the…

We show that descriptive complexity's result extends in High Order Logic to capture the expressivity of Turing Machine which have a finite number of alternation and whose time or space is bounded by a finite tower of exponential. Hence we…

We prove that the MSO+U logic is compositional in the following sense: whether an MSO+U formula holds in a tree T depends only on MSO+U-definable properties of the root of T and of subtrees of T starting directly below the root. Another…

Several types of term rewriting systems can be distinguished by the way their rules overlap. In particular, we define the classes of prefix, suffix, bottom-up and top-down systems, which generalize similar classes on words. Our aim is to…

Topological behavior, such as chaos, irreducibility, and mixing of a one-sided shift of finite type, is well elucidated. Meanwhile, the investigation of multidimensional shifts, for instance, textile systems is difficult and only a few…

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…

The first two successful predictions for amorphous solid experiments by tunneling-two-level-system (TTLS) was phonon echo and saturation phenomena. In this paper by generalizing TTLS to infinite-level-system model with certain randomness…

Transition-based top-down parsing with pointer networks has achieved state-of-the-art results in multiple parsing tasks, while having a linear time complexity. However, the decoder of these parsers has a sequential structure, which does not…

Chain of thought is a natural inference-time method for increasing the computational power of transformer-based large language models (LLMs), but comes at the cost of sequential decoding. Are there more efficient alternatives to expand a…

We study the topological structure of random geometric forests $G$ in the Euclidean plane under mild assumptions: non-crossing edges, stationarity, and finite edge intensity. The framework covers a broad range of constructions, including…

In a recent paper we introduced a new framework for the study of call by need computations to normal form and root-stable form in term rewriting. Using elementary tree automata techniques and ground tree transducers we obtained simple…

We investigate the tree-to-tree functions computed by "affine $\lambda$-transducers": tree automata whose memory consists of an affine $\lambda$-term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati's…

Phrase structure trees have a hierarchical structure. In many subjects, most notably in Taxonomy such tree structures have been studied using ultrametrics. Here syntactical hierarchical phrase trees are subject to a similar analysis, which…

Syntactic Language Models (SLMs) can be trained efficiently to reach relatively high performance; however, they have trouble with inference efficiency due to the explicit generation of syntactic structures. In this paper, we propose a new…

We study power-set operations on classes of trees and tree algebras. Our main result consists of a distributive law between the tree monad and the upwards-closed power-set monad, in the case where all trees are assumed to be linear. For…

For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…

This paper presents a new approach to regulation of grammars. It divides the derivation trees generated by grammars into two sections-generative and conclusive (the conclusion). The former encompasses generation of symbols up till the…