Exact solution of the Bernoulli matching model of sequence alignment

TL;DR

This paper provides an exact analytical solution for the Bernoulli sequence alignment model by mapping it to a known exclusion process, deriving the distribution of the longest common subsequence length, and analyzing its asymptotic behavior.

Contribution

It introduces a novel exact solution for the Bernoulli sequence alignment model using mappings to exclusion processes and Bethe ansatz techniques, connecting finite-size results to asymptotic limits.

Findings

Exact distribution of LCS length derived

Finite-size results connected to asymptotic behavior

Analytical expressions obtained using Bethe ansatz

Abstract

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.