Directed acyclic subsequence graph—Overview

The subsequence matching problem is to decide, for given strings S and T, whether S is a subsequence of T. The string S is called the pattern and the string T the text. We consider the case of multiple texts and show how to solve the subsequence matching problem in time linear in the length of the pattern. For this purpose we build an automaton that accepts all subsequences of given texts. This automaton is called the Directed Acyclic Subsequence Graph (DASG). We prove an upper bound for its number of states. Furthermore, we consider a modification of the subsequence matching problem: given a string S and a finite language L, we are to decide whether S is a subsequence of any string in L. We suppose that a finite automaton accepting L is given and present an algorithm for building the DASG for language L. We also mention applications of the DASG to some problems related to subsequences.