Related papers: Commutative positive varieties of languages
We introduce an invariant of varieties in positive characteristic which generalizes the a-number of an abelian variety. We calculate it in some examples and discuss its meaning for moduli.
A permutation of n letters is k-prolific if each (n-k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations…
We study commutative associative polynomial operations $\mathbb{A}^n\times\mathbb{A}^n\to\mathbb{A}^n$ with unit on the affine space $\mathbb{A}^n$ over an algebraically closed field of characteristic zero. A classification of such…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
The world's languages exhibit certain so-called typological or implicational universals; for example, Subject-Object-Verb (SOV) languages typically use postpositions. Explaining the source of such biases is a key goal of linguistics. We…
We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…
Weighted automata are nondeterministic automata with numerical weights on transitions. They can define quantitative languages $L$ that assign to each word $w$ a real number $L(w)$. In the case of infinite words, the value of a run is…
Our goal is to classify all generically transitive actions of commutative unipotent groups on flag varieties up to conjugation. We establish relationship between this problem and classification of multiplications with certain properties on…
Languages are continuously undergoing changes, and the mechanisms that underlie these changes are still a matter of debate. In this work, we approach language evolution through the lens of causality in order to model not only how various…
We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…
An upward (resp. downward) digitally convex word is a binary word that best approximates from below (resp. from above) an upward (resp. downward) convex curve in the plane. We study these words from the combinatorial point of view,…
In this chapter we provide an overview of computational modeling for semantic change using large and semi-large textual corpora. We aim to provide a key for the interpretation of relevant methods and evaluation techniques, and also provide…
Many different deletion operations are investigated applied to languages accepted by one-way and two-way deterministic reversal-bounded multicounter machines, deterministic pushdown automata, and finite automata. Operations studied include…
We consider two-variable first-order logic on finite words with a fixed number of quantifier alternations. We show that all languages with a neutral letter definable using the order and finite-degree predicates are also definable with the…
Code-switching, the alternation of languages within a conversation or utterance, is a common communicative phenomenon that occurs in multilingual communities across the world. This survey reviews computational approaches for code-switched…
We define a closure operation for ideals in a commutative ring which has all the good properties of solid closure (at least in the case of equal characteristic) but such that also every ideal in a regular ring is closed. This gives in…
This article is a survey of closure operations on ideals in commutative rings, with an emphasis on structural properties and on using tools from one part of the field to analyze structures in another part. The survey is broad enough to…
Dynamic languages are praised for their flexibility and expressiveness, but static analysis often yields many false positives and verification is cumbersome for lack of structure. Hence, unit testing is the prevalent incomplete method for…
We introduce a guessing game, permutation Wordle, in which a guesser attempts to recover a hidden permutation in $S_n$. In each round, the guesser guesses a permutation (using information from previous rounds) and is told which entries of…
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.