Related papers: Bounded Languages Described by GF(2)-grammars
We introduce several classes of array languages obtained by generalising Angluin's pattern languages to the two-dimensional case. These classes of two-dimensional pattern languages are compared with respect to their expressive power and…
In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations…
A $GL_d$-pseudocharacter is a function from a group $\Gamma$ to a ring $k$ satisfying polynomial relations which make it "look like" the character of a representation. When $k$ is an algebraically closed field, Taylor proved that…
Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems. We formulate…
We introduce regular language states, a family of quantum many-body states. They are built from a special class of formal languages, called regular, which has been thoroughly studied in the field of computer science. They can be understood…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We define the notion of a semicharacter of a group G : A function from the group to C*, whose restriction to any abelian subgroup is a homomorphism. We conjecture that for any finite group, the order of the group of semicharacters is…
The vertices of a finite state system are usually a subset of the natural numbers. Most algorithms relative to these systems only use this fact to select vertices. For infinite state systems, however, the situation is different: in…
Graph Neural Networks (GNNs) have demonstrated significant success in learning from graph-structured data across various domains. Despite their great successful, one critical challenge is often overlooked by existing works, i.e., the…
Given a group word $w$ and a group $G$, the set of $w$-values in $G$ is denoted by $G_w$ and the verbal subgroup $w(G)$ is the one generated by $G_w$. In the present paper we consider profinite groups admitting a word $w$ such that the…
We define a degenerate affine version of the walled Brauer algebra, that has the same role plaid by the degenerate affine Hecke algebra for the symmetric group algebra. We use it to prove a higher level mixed Schur-Weyl duality for gl_N. We…
Motivated by recent connections to factorised databases, we analyse the efficiency of representations by context free grammars (CFGs). Concretely, we prove a recent conjecture by Kimelfeld, Martens, and Niewerth (ICDT 2025), that for finite…
There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but subclasses have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties.…
Since language models are used to model a wide variety of languages, it is natural to ask whether the neural architectures used for the task have inductive biases towards modeling particular types of languages. Investigation of these biases…
Quadratic algebras related to the reflection equations are introduced. They are quantum group comodule algebras. The quantum group $F_q(GL(2))$ is taken as the example. The properties of the algebras (center, representations, realizations,…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
We introduce a new class of algebras, called reconstruction algebras, and present some of their basic properties. These non-commutative rings dictate in every way the process of resolving the Cohen-Macaulay singularities C^2/G where G is a…
Pregroup grammars were developed in 1999 and stayed Lambek's preferred algebraic model of grammar. The set-theoretic semantics of pregroups, however, faces an ambiguity problem. In his latest book, Lambek suggests that this problem might be…