The size of subsequence automaton

Abstract

Given a set of strings, the subsequence automaton accepts all subsequences of these strings. We derive a lower bound for the maximum number of states of this automaton. We prove that the size of the subsequence automaton for a set of k strings of length n is Ω ( n k / ( k + 1 ) k k ! ) for any k ⩾ 1 . It solves an open problem because only the case k ⩽ 2 was shown before.