Related papers: Novel Constructions of Words with Strong Avoidance…
This article is an introduction to formal languages from the point of view of combinatorial group theory. Group theoretic applications are included and language classes are defined algebraically.
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
We study a conjecture linking ultimate periodicity of infnite words to the existence of colorings on finite words avoiding monochromatic factorisation of suffixes, with the extra condition that the ordered concatenation of elements of this…
I propose a variable-free treatment of dynamic semantics. By "dynamic semantics" I mean analyses of donkey sentences ("Every farmer who owns a donkey beats it") and other binding and anaphora phenomena in natural language where meanings of…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
We consider three aspects of avoiding large squares in infinite binary words. First, we construct an infinite binary word avoiding both cubes xxx and squares yy with |y| >= 4; our construction is somewhat simpler than the original…
We develop necessary and sufficient conditions and a novel provably consistent and efficient algorithm for discovering topics (latent factors) from observations (documents) that are realized from a probabilistic mixture of shared latent…
In this paper, we provide a new characterization of uniformly recurrent words with finite defect based on a relation between the palindromic and factor complexity. Furthermore, we introduce a class of morphisms P_ret closed under…
The purpose of this paper is to investigate the connection between the Lotka-Volterra system and combinatorics. We study several context-free grammars associated with the Lotka-Volterra system. Some combinatorial arrays, involving the…
The method we have applied in "A. Bernini, L. Ferrari, R. Pinzani, Enumerating permutations avoiding three Babson-Steingrimsson patterns, Ann. Comb. 9 (2005), 137--162" to count pattern avoiding permutations is adapted to words. As an…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
Let $w$ be a word in a free group. A few years ago, Magee and the first named author discovered that the stable commutator length (scl) of $w$, a well-known topological invariant, can also be defined in terms of certain Fourier coefficients…
We present a method for the enumeration of restricted words over a finite alphabet. Restrictions are described through the inclusion or exclusion of suitable building blocks used to construct the words by concatenation. Our approach, which…
The notion of almost periodicity nontrivially generalizes the notion of periodicity. Strongly almost periodic sequences (=uniformly recurrent infinite words) first appeared in the field of symbolic dynamics, but then turned out to be…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
We study subshift that arise by excluding words of length two from Dyck shifts. The words that are to be excluded are taken from a finite set that is not literal-uniform.
We consider the language of $\Delta_0$-formulas with list terms interpreted over hereditarily finite list superstructures. We study the complexity of reasoning in extensions of the language of $\Delta_0$-formulas with non-standard list…
We study the properties of the uncountable set of Stewart words. These are Toeplitz words specified by infinite sequences of Toeplitz patterns of the form $\alpha\beta\gamma$, where $\alpha,\beta,\gamma$ is any permutation of the symbols…
In this paper, we study the pattern occurrence in $k$-ary words. We prove an explicit upper bound on the number of $k$-ary words avoiding any given pattern using a random walk argument. Additionally, we reproduce several already known…
Construction grammar posits that constructions, or form-meaning pairings, are acquired through experience with language (the distributional learning hypothesis). But how much information about constructions does this distribution actually…