Longest common subsequences in binary sequences

TL;DR

This paper investigates the asymptotic behavior of the longest common subsequence length in binary sequences, focusing on the limit of expected LCS as sequence lengths grow and its relation to the Chvatal-Sankoff constant.

Contribution

It analyzes the limiting behavior of the expected LCS in binary sequences and explores its connection to the Chvatal-Sankoff constant, advancing understanding of sequence similarity measures.

Findings

Characterizes the limit of expected LCS for scaled sequence lengths.

Establishes a relationship between the limit function and the Chvatal-Sankoff constant.

Provides insights into the asymptotic properties of binary sequence comparison.

Abstract

Given two {0,1}-sequences X and Y of lengths m and n, respectively, we write L(X,Y) to denote the length of the longest common subsequence (LCS) of X and Y, and write L(m,n) to denote the expected value of L(X,Y) when X and Y are random sequences. We study the value of the function z -> lim L(nz,n)/n (as n -> infinity) and the relation of this function to the outstanding problem of computing the Chvatal-Sankoff constant lim L(n,n)/n.