Related papers: Languages of general interval exchange transformat…
We investigate mechanisms for language change within a framework where an unconventional signal for a meaning is first innovated, and then subsequently propagated through a speech community to replace the existing convention. We appeal to…
Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…
In this article we undertake a study of extension complexity from the perspective of formal languages. We define a natural way to associate a family of polytopes with binary languages. This allows us to define the notion of extension…
In [Fortini et al., Stoch. Proc. Appl. 100 (2002), 147--165] it is demonstrated that a recurrent Markov exchangeable process in the sense of Diaconis and Freedman is essentially a partially exchangeable process in the sense of de Finetti.…
Programming languages are engineered languages that allow to instruct a machine and share algorithmic information; they have a great influence on the society since they underlie almost every information technology artefact, and they are at…
We show the following generalizations of the de Finetti--Hewitt--Savage theorem: Given an exchangeable sequence of random elements, the sequence is conditionally i.i.d. if and only if each random element admits a regular conditional…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
We consider symbolic flows over finite alphabets and study certain kinds of repetitions in these sequences. Positive and negative results for the existence of such repetitions are given for codings of interval exchange transformations and…
We extend de Finetti's (1937) notion of exchangeability to finite and countable sequences of variables, when a subject's beliefs about them are modelled using coherent lower previsions rather than (linear) previsions. We prove…
A quantitative method is suggested, where meanings of words, and grammatic rules about these, of a vocabulary are represented by real numbers. People meet randomly, and average their vocabularies if they are equal; otherwise they either…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
To what extent can neural network models learn generalizations about language structure, and how do we find out what they have learned? We explore these questions by training neural models for a range of natural language processing tasks on…
Given a symmetric exchange of three intervals, we provide a detailed description of the return times to a subinterval and the corresponding itineraries. We apply our results to morphisms fixing words coding non-degenerate three interval…
An interval translation map (ITM) is a piece-wise translation $T \colon I \to I$ defined on a finite partition $I_1, \ldots, I_r$ of an interval $I$ into $r \ge 2$ subintervals. In contrast to classical interval exchange transformations…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
This paper is about pregroup models of natural languages, and how they relate to the explicitly categorical use of pregroups in Compositional Distributional Semantics and Natural Language Processing. These categorical interpretations make…
Workflows constitute an important language to represent knowledge about processes, but also increasingly to reason on such knowledge. On the other hand, there is a limit to which time constraints between activities can be expressed.…
Roth type irrational rotation numbers have several equivalent arithmetical characterizations as well as several equivalent characterizations in terms of the dynamics of the corresponding circle rotations. In this paper we investigate how to…
Multilinguality is crucial for extending recent advancements in language modelling to diverse linguistic communities. To maintain high performance while representing multiple languages, multilingual models ideally align representations,…