Subsequence Automata with Default Transitions

Abstract. Let S be a string of length n with characters from an alphabet of size σ. The subsequence automaton (often called the directed acyclic subsequence graph) is the minimal deterministic finite automaton accepting all subsequences of S. A straightforward construction shows that the size (number of states and transitions) of the subsequence automaton is O(nσ) and that this bound is asymptotically optimal. In this paper, we consider subsequence automata with default transitions, that is, special transitions to be taken only if none of the regular transitions match the current character, and which do not consume the current character. We show that with default transitions, much smaller subsequence automata are possible, and provide a full trade-off between the size of the automaton and the delay, i.e., the maximum number of default transition followed before consuming a character. Specifically, given any integer parameter k, 1 < k ≤ σ, we present a subsequence automaton w...

• Type: Journal
• Year: 2016
• Where: SOFSEM
• Authors: Philip Bille, Inge Li Gørtz, Frederik Rye Skjoldjensen
• Keywords: SOFSEM 2016, Theoretical Computer Science