The Shift-Match Number and String Matching Probabilities for Binary Sequences

TL;DR

This paper introduces the shift-match number for binary strings and derives formulas for the probability of a string appearing as a subsequence in longer strings, highlighting the importance of this new measure in string matching probabilities.

Contribution

It defines the shift-match number and establishes its role in determining string matching probabilities, providing a novel analytical tool for binary sequence analysis.

Findings

String matching probabilities depend on shift-match number

Shift-match number classifies strings into equivalence classes

Probabilities are computed in terms of shift-match numbers

Abstract

We define the ``shift-match number'' for a binary string and we compute the probability of occurrence of a given string as a subsequence in longer strings in terms of its shift-match number. We thus prove that the string matching probabilities depend not only on the length of shorter strings, but also on the equivalence class of the shorter string determined by its shift-match number.