Related papers: Around Context-Free Grammars -- a Normal Form, a R…
The central role of the lexicon in Meaning-Text Theory (MTT) and other dependency-based linguistic theories cannot be replicated in linguistic theories based on context-free grammars (CFGs). We describe Tree Adjoining Grammar (TAG) as a…
These lecture notes contain an exposition of basic ideas of K-theory and cyclic cohomology. I begin with a list of examples of various situations in which the K-functor of Grothendieck appears naturally, including the rudiments of the…
I propose a class of non-positional numeral systems where numbers are represented by Dyck words, with the systems arising from a recursive extension of prime factorization. After describing two proper subsets of the Dyck language capable of…
We study a class of rational Dyck paths with slope (2m+1)/2 corresponding to factor-free Dyck words, as introduced by P. Duchon. We show that, for the slopes considered in this paper, the language of factor-free Dyck words is generated by…
The article gives the second part of the treatise on Regular Algebraic $K$-theory (Sections V & VI) of the author. Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected to (but different from)…
The memory of a deque (double ended queue) automaton is more general than a queue or two stacks; to avoid overgeneralization, we consider quasi-real-time operation. Normal forms of such automata are given. Deque languages form an AFL but…
We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call {\em semidirectional}. In semidirectional Lambek calculus $\SDL$ there is an additional non-directional abstraction rule…
Given any digraph $D$ without loops or multiple arcs, there is a natural construction of a semigroup $\langle D\rangle$ of transformations. To every arc $(a,b)$ of $D$ is associated the idempotent transformation $(a\to b)$ mapping $a$ to…
We show that a field $K$ is model complete (in the language of rings) if and only if the Heisenberg group $H(K)$ is model complete (in the language of groups). To show that, we extend Levchuk's result about automorphisms of $H(K)$ to the…
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to…
Given a simple digraph $D$ on $n$ vertices (with $n\ge2$), there is a natural construction of a semigroup $\langle D\rangle$ associated with $D$. For any edge $(a,b)$ of $D$, let $a\to b$ be the idempotent of defect $1$ mapping $a$ to $b$…
In this work, we introduce a new notion for representing graph classes with formal languages. In contrast to the seminal work by Kitaev and Pyatkin to represent graphs by words, we use formal binary languages in order to have a set of…
Series-parallel (SP) graphs are binary edge-labeled graphs with a designated source and target vertex, built using serial and parallel composition. A set of graphs is recognizable if membership depends only on its image under a homomorphism…
This report is a survey of the relationships between various state-of-the-art neural network architectures and formal languages as, for example, structured by the Chomsky Language Hierarchy. Of particular interest are the abilities of a…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…
Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…
A common question when studying a class of context-free grammars is whether equivalence is decidable within this class. We answer this question positively for the class of Clark-congruential grammars, which are of interest to grammatical…
Since the random language model was proposed by E. DeGiuli [Phys. Rev. Lett. 122, 128301], language models have been investigated intensively from the viewpoint of statistical mechanics. Recently, the existence of a…