相关论文: Counting and Verifying Abelian Border Arrays of Bi…
An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $\Theta(n^2)$ distinct factors, and there exist words of length $n$ containing $\Theta(n^2)$ distinct…
We show that the number of prefix normal binary words of length $n$ is $2^{n-\Theta((\log n)^2)}$. We also show that the maximum number of binary words of length $n$ with a given fixed prefix normal form is $2^{n-O(\sqrt{n\log n})}$.
Two finite words $u$ and $v$ are called Abelian equivalent if each letter occurs equally many times in both $u$ and $v$. The abelian closure $\mathcal{A}(\mathbf{x})$ of (the shift orbit closure of) an infinite word $\mathbf{x}$ is the set…
We derive formulas for $(i)$ the number of toroidal $n\times n$ binary arrays, allowing rotation of rows and/or columns as well as matrix transposition, and $(ii)$ the number of toroidal $n\times n$ binary arrays, allowing rotation and/or…
Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word…
A formula for the number of toroidal m x n binary arrays, allowing rotation of the rows and/or the columns but not reflection, is known. Here we find a formula for the number of toroidal m x n binary arrays, allowing rotation and/or…
We give an explicit construction of length-$n$ binary codes capable of correcting the deletion of two bits that have size $2^n/n^{4+o(1)}$. This matches up to lower order terms the existential result, based on an inefficient greedy choice…
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. Our main result is an online algorithm that, given a word…
Since Cocke and Minsky proved 2-tag systems universal, they have been extensively used to prove the universality of numerous computational models. Unfortunately, all known algorithms give universal 2-tag systems that have a large number of…
We consider the problem of finding repetitive structures and inherent patterns in a given string $\s{s}$ of length $n$ over a finite totally ordered alphabet. A border $\s{u}$ of a string $\s{s}$ is both a prefix and a suffix of $\s{s}$…
We address the problem of efficient verification of multi-threaded programs running over Total Store Order (TSO) memory model. It has been shown that even with finite data domain programs, the complexity of control state reachability under…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their…
Upper bounds on the maximum number of minimal codewords in a binary code follow from the theory of matroids. Random coding provide lower bounds. In this paper we compare these bounds with analogous bounds for the cycle code of graphs. This…
Given a word $w$ and a Parikh vector $\mathcal{P}$, an abelian run of period $\mathcal{P}$ in $w$ is a maximal occurrence of a substring of $w$ having abelian period $\mathcal{P}$. We give an algorithm that finds all the abelian runs of…
Let $x \in \R$ be given. As we know the, amount of bits needed to binary code $x$ with given accuracy ($h \in \R$) is approximately $ \m_{h}(x) \approx \log_{2}(\max {1, |\frac{x}{h}|}). $ We consider the problem where we should translate…
Word segmentation is the task of inserting or deleting word boundary characters in order to separate character sequences that correspond to words in some language. In this article we propose an approach based on a beam search algorithm and…
We show an asymptotic 2/3-competitive strategy for the bin covering problem using O(b+log n) bits of advice, where b is the number of bits used to encode a rational value and n is the length of the input sequence.
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…