Related papers: Scattered context-free linear orderings
Existing technology can parse arbitrary context-free grammars, but only a single, static grammar per input. In order to support more powerful syntax-extension systems, we propose reflective grammars, which can modify their own syntax during…
A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Previous research has demonstrated that natural language explanations provide valuable inductive biases that guide models, thereby improving the generalization ability and data efficiency. In this paper, we undertake a systematic…
In the present paper we show that distributional information is particularly important when considering concept availability under implicit language learning conditions. Based on results from different behavioural experiments we argue that…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given…
We measured the correlation of the times between successive flaps of a flag for a variety of wind speeds and found no evidence of low dimensional chaotic behavior in the return maps of these times. We instead observed what is best modeled…
This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted…
It is shown that as far as the linear diffusion equation meets both time- and space- translational invariance, the time dependence of a moment of degree $\alpha$ is a polynomial of degree at most equal to $\alpha$, while all connected…
Natural language exhibits statistical dependencies at a wide range of scales. For instance, the mutual information between words in natural language decays like a power law with the temporal lag between them. However, many statistical…
We study the time taken by a language learner to correctly identify the meaning of all words in a lexicon under conditions where many plausible meanings can be inferred whenever a word is uttered. We show that the most basic form of…
Scattering through natural porous formations (by far the most ubiquitous example of disordered media) represents a formidable tool to identify effective flow and transport properties. In particular, we are interested here in the scattering…
We consider the nonlinear Schr{\"o}dinger equation with a short-range external potential, in a semi-classical scaling. We show that for fixed Planck constant, a com-plete scattering theory is available, showing that both the potential and…
One of the most interesting questions concerning hierarchical control of discrete-event systems with partial observations is a condition under which the language observability is preserved between the original and the abstracted plant.…
We present a probabilistic language model for time-stamped text data which tracks the semantic evolution of individual words over time. The model represents words and contexts by latent trajectories in an embedding space. At each moment in…
The rank of a scattered $\mathbb{F}_q$-linear set of $\mathrm{PG}(r-1,q^n)$, $rn$ even, is at most $rn/2$ as it was proved by Blokhuis and Lavrauw. Existence results and explicit constructions were given for infinitely many values of $r$,…