Related papers: Two-dimensional Dyck words

In this work, we establish a direct connection between supplemented Dyck language and the signed expectation value of chains of second quantization operators relatively to the physical vacuum and relatively to a one-determinant state.…

This paper proposes a novel framework connecting fermionic second quantization and Dyck languages. By defining translations of creation and annihilation operators using bracket alphabets, the study establishes nullity criteria for…

We introduce a normal form for context-free grammars, called Dyck normal form. This is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired nonterminals.…

We study various aspects of Dyck words appearing in binary sequences, where $0$ is treated as a left parenthesis and $1$ as a right parenthesis. We show that binary words that are $7/3$-power-free have bounded nesting level, but this no…

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…

Despite their impressive performance in NLP, self-attention networks were recently proved to be limited for processing formal languages with hierarchical structure, such as $\mathsf{Dyck}_k$, the language consisting of well-nested…

The main goal of this work is to establish a bijection between Dyck words and a family of Eulerian digraphs. We do so by providing two algorithms implementing such bijection in both directions. The connection between Dyck words and Eulerian…

A subfamily of Dyck words called tight Dyck words is seen to correspond, via a "castling" procedure, to the vertex set of an ordered tree $T$. From $T$, a "blowing" operation recreates the whole family ol Dyck words. The vertices of $T$ can…

The article deals with a lexicographic order in various sequences. Consider the axiomatic of lexicographic series, based on the properties of the natural numbers. Elements of the set are ordered first the code length; further in each sign…

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…

The Dyck language, which consists of well-balanced sequences of parentheses, is one of the most fundamental context-free languages. The Dyck edit distance quantifies the number of edits (character insertions, deletions, and substitutions)…

We deal with a normal form for context-free grammars, called Dyck normal form. This normal form is a syntactical restriction of the Chomsky normal form, in which the two nonterminals occurring on the right-hand side of a rule are paired…

In this paper we consider the problem of deciding membership in Dyck languages, a fundamental family of context-free languages, comprised of well-balanced strings of parentheses. In this problem we are given a string of length $n$ in the…

We define a set of binary matrices where any two of them can not be placed one on the other in a way such that the corresponding entries coincide. The rows of the matrices are obtained by means of Dyck words. The cardinality of the set of…

Let $0<k\in\mathbb{Z}$. The anchored Dyck words of length $n=2k+1$ (obtained by prefixing a 0-bit to each Dyck word of length $2k$ and used to reinterpret the Hamilton cycles in the odd graph $O_k$ and the middle-levels graph $M_k$ found by…

Valid hook configurations are combinatorial objects used to understand West's stack sorting map as well as cumulants in noncommutative probability theory. We show a bijection between reduced valid hook configurations on 312-avoiding…

Let $0<k\in\mathbb{Z}$. We zipper-merge integer compositions with sums $k$ and $k+1$, equal number of parts and initial entries equal at least to 1 and 2, respectively. This yields bitstrings with two initial zeros, $k-1$ remaining zeros…

Transforming a sentence into a two-dimensional (2D) representation (e.g., the table filling) has the ability to unfold a semantic plane, where an element of the plane is a word-pair representation of a sentence which may denote a possible…

Dyck reachability is the standard formulation of a large domain of static analyses, as it achieves the sweet spot between precision and efficiency, and has thus been studied extensively. Interleaved Dyck reachability (denoted $D_k\odot…

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…