Related papers: Expected Number of Distinct Subsequences in Random…
The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has…
We investigate the longest common substring problem for encoded sequences and its asymptotic behaviour. The main result is a strong law of large numbers for a re-scaled version of this quantity, which presents an explicit relation with the…
One of the key requirement of many schemes is that of random numbers. Sequence of random numbers are used at several stages of a standard cryptographic protocol. A simple example is of a Vernam cipher, where a string of random numbers is…
Two closely related discrete probability distributions are introduced. In each case the support is a set of vectors in $\mathbb{R}^n$ obtained from the partitions of the fixed positive integer $n$. These distributions arise naturally when…
The nature of the alignment with gaps corresponding to a longest common subsequence (LCS) of two independent iid random sequences drawn from a finite alphabet is investigated. It is shown that such an optimal alignment typically matches…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
The main subject of the paper is everywhere complex sequences. An everywhere complex sequence is a sequence that does not contain substrings of Kolmogorov complexity less than $\alpha n-O(1)$ where $n$ is the length of substring and…
The theory of sequences, supported by many SMT solvers, can model program data types including bounded arrays and lists. Sequences are parameterized by the element data type and provide operations such as accessing elements, concatenation,…
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of…
The topic of this paper is the distributed and incremental generation of long executions of concurrent systems, uniformly or more generally with weights associated to elementary actions. Synchronizing sequences of letters on alphabets…
There are at present two known string theories in $(2,2)$ dimensions. One of them is the well known $N=2$ string, and the other one is a more recently constructed $N=1$ spacetime supersymmetric string. They are both based on certain…
This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time…
We study codes that can detect the exact number of deletions and insertions in concatenated binary strings. We construct optimal codes for the case of detecting up to $\del$ deletions. We prove the optimality of these codes by deriving a…
Cosmic strings are predicted by many field-theory models, and may have been formed at a symmetry-breaking transition early in the history of the universe, such as that associated with grand unification. They could have important…
This paper questions the generally accepted assumption that one can make a random choice that is independent of the rest of the universe. We give a general description of any setup that could be conceived to generate random numbers. Based…
We study the average edit distance between two random strings. More precisely, we adapt a technique introduced by Lueker in the context of the average longest common subsequence of two random strings to improve the known upper bound on the…
We consider two independent binary i.i.d. random strings $X$ and $Y$ of equal length $n$ and the optimal alignments according to a symmetric scoring functions only. We decompose the space of scoring functions into five components. Two of…
In this paper we initiate the study of computing a maximal (not necessarily maximum) repeating pattern in a single input string, where the corresponding problems have been studied (e.g., a maximal common subsequence) only in two or more…
We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are…