Related papers: A Gray Code for cross-bifix-free sets
We present a construction of 1-perfect binary codes, which gives a new lower bound on the number of such codes. We conjecture that this lower bound is asymptotically tight.
Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new…
We consider sets of positive integers containing no sum of two elements in the set and also no product of two elements. We show that the upper density of such a set is strictly smaller than 1/2 and that this is best possible. Further, we…
We present an encoding and decoding scheme for constant weight sequences, that is, given an information sequence, the construction results in a sequence of specific weight within a certain range. The scheme uses a prefix design that is…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next…
We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…
This paper introduces almost partitionable sets to generalize the known concept of partitionable sets. These notions provide a unified frame to construct $\mathbb{Z}$-cyclic patterned starter whist tournaments and cyclic balanced sampling…
We describe a compression-aware method to compute all-vs-all maximal exact matches (MEM) among strings of a repetitive collection $\mathcal{T}$. The key concept in our work is the construction of a fully-balanced grammar $\mathcal{G}$ from…
In this paper we introduce a method to detect words or phrases in a given sequence of alphabets without knowing the lexicon. Our linear time unsupervised algorithm relies entirely on statistical relationships among alphabets in the input…
In this paper, we introduce a standard generator matrix for mixed-alphabet linear codes over finite chain rings. Furthermore, we show that, when one has a linear complementary pair (LCP) of mixed-alphabet linear codes, both codes are…
We present a simple encoding for unlabeled noncrossing graphs and show how its latent counterpart helps us to represent several families of directed and undirected graphs used in syntactic and semantic parsing of natural language as…
We address the recently suggested problem of causal lossless coding of a randomly arriving source samples. We construct variable-to-fixed coding schemes and show that they outperform the previously considered fixed-to-variable schemes when…
Several classical constructions illustrate the fact that the chromatic number of a graph can be arbitrarily large compared to its clique number. However, until very recently, no such construction was known for intersection graphs of…
The Suffix Array is a classic text index enabling on-line pattern matching queries via simple binary search. The main drawback of the Suffix Array is that it takes linear space in the text's length, even if the text itself is extremely…
Using the theory of Properly Embedded Graphs developed in an earlier work we define an involutory duality on the set labeled non-crossing trees that lifts the obvious duality in the set of unlabeled non-crossing trees. The set of…
The set of idempotents of any semigroup carries the structure of a biordered set, which contains a great deal of information concerning the idempotent generated subsemigroup of the semigroup in question. This leads to the construction of a…
Circular words are cyclically ordered finite sequences of letters. We give a computer-free proof of the following result by Currie: square-free circular words over the ternary alphabet exist for all lengths $l$ except for 5, 7, 9, 10, 14,…
A graph in which all minimal zero forcing sets are in fact minimum size is called ``well-forced." This paper characterizes well-forced trees and presents an algorithm for determining which trees are well-forced. Additionally, we…
We give the first two algorithms to enumerate all binary words of $\{0,1\}^\ell$ (like Gray codes) while ensuring that the delay and the auxiliary space is independent from $\ell$, i.e., constant time for each word, and constant memory in…