Operations on DASG

Abstract

Directed Acyclic Subsequence Graph (DASG) is an automaton that accepts all subsequences of a given string T. DASG allows us to decide whether a string S is a subsequence of T in O(|S|) time where |S| is the length of S. We show that if we slightly modify the string T, it is possible to get the DASG for the modified string from the original DASG. For this purpose we define these operations on DASG: adding a state on the left, deleting a state on left, adding a state on the right, deleting a state on the right, adding an inner state, deleting an inner state and replacing a transition label. For each of these operations we describe the modification of DASG and the proof of correctness.