Related papers: The non-abelian squares are not context-free
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all…
An uncountable $\aleph_1$-free group cannot admit a Polish group topology but an uncountable $\aleph_1$-free abelian group can, as witnessed, for example, by the Baer-Specker group $\mathbb{Z}^\omega$; more strongly, $\mathbb{Z}^\omega$ is…
We construct an abstract elementary class $K_1$ of torsion-free abelian groups such that $K_1$ is not $(<\aleph_0)$-tame but is $\aleph_0$-tame. This answers a question of [BoVa17]. Furthermore, for every regular uncountable cardinal $\mu$…
Context-free grammar simplification is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of the fact that…
We prove that for any sequence of binary alphabets $\mathcal{A}_1,\mathcal{A}_2,\dots$, there exists a cube-free word $c_1c_2\dots$ so that $c_1\in\mathcal{A}_1,c_2\in\mathcal{A}_2,\dots$. In particular, for every $n$, there are at least…
Pumping lemmas are created to prove that given languages are not belong to certain language classes. There are several known pumping lemmas for the whole class and some special classes of the context-free languages. In this paper we prove…
Recently, the author characterized all artinian square-free rings with identity. Here, those results are extended to the setting of rings with local units. We use this characterization of square-free rings to derive many results similar to…
We give in this paper additional answers to questions of Lescow and Thomas [Logical Specifications of Infinite Computations, In:"A Decade of Concurrency", Springer LNCS 803 (1994), 583-621], proving new topological properties of omega…
We completely characterize the words that can be avoided in infinite squarefree ternary words.
The new generalization of the gauge interaction for the bosonic strings is found. We consider some quasiequivariant maps from the space of metrics on the worldsheet to the space of $n$-tuples of one- and two-dimensional loops. The…
This paper is a continuation of the study of topological properties of omega context free languages (omega-CFL). We proved before that the class of omega-CFL exhausts the hierarchy of Borel sets of finite rank, and that there exist some…
Context-free language theory is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of fundamental results related…
We prove that arboreal Galois extensions of number fields are never abelian for post-critically finite rational maps and non-preperiodic base points. For polynomials, this establishes a new class of known cases of a conjecture of…
We prove (using grammars) that the free inverse monoid of every finite rank has co-context-free word problem. Equivalently, the co-word problem of the free inverse monoid of every finite rank is context-free.
Semantically non-compositional phrases constitute an intriguing research topic in Natural Language Processing. Semantic non-compositionality --the situation when the meaning of a phrase cannot be derived from the meaning of its components,…
We study words that barely avoid repetitions, for several senses of "barely". A squarefree (respectively, overlap-free, cubefree) word is irreducible if removing any one of its interior letters creates a square (respectively, overlap,…
A graph is said to be word-representable if there exists a word over its vertex set such that any two vertices are adjacent if and only if they alternate in the word. If no such word exists, the graph is non-word-representable. In the…
We give in this paper some squares of abelian surfaces that are counterexamples to a conjecture formulated by Zhang about the intersection of subvarieties and preperiodic points.
In this paper we prove several results on normal forms for linear displacement context-free grammars. The results themselves are rather simple and use well-known techniques, but they are extensively used in more complex constructions.…
We give a criterion in terms of period matrices for an arbitrary polarized abelian variety to be non-simple. Several examples are worked out.