Dynamic Membership for Regular Languages

15 Feb 2021 Antoine Amarilli Louis Jachiet Charles Paperman

We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under substitution edits on w. We consider this problem on the unit cost RAM model with logarithmic world length, where the problem always has a solution in O(log |w| / log log |w|). We show that the problem is in O(log log |w|) for languages in an algebraically-defined class QSG, and that it is in O(1) for another class QLZG... (read more)

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Categories


  • FORMAL LANGUAGES AND AUTOMATA THEORY
  • DATA STRUCTURES AND ALGORITHMS