State complexity of operations on input-driven pushdown automata

: Alexander Okhotin, Kai Salomaa

Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE

: 2017

: Journal of Computer and System Sciences

: JOURNAL OF COMPUTER AND SYSTEM SCIENCES

: J COMPUT SYST SCI

: 86

: 207

: 228

: 22

: 0022-0000

: 1090-2724

DOI: https://doi.org/10.1016/j.jcss.2017.02.001(external)

The family of languages recognized by deterministic input -driven pushdown automata (IDPDA; a.k.a. visibly pushdown automata, a.k.a. nested word automata) is known to be closed under concatenation, Kleene star and reversal (under natural assumptions on the partition of the alphabet). As shown by Alur and Madhusudan (2004) [2], the Kleene star and the reversal of an n -state IDPDA can be represented by an IDPDA with 2(O(n2)) states, while concatenation of an m -state and an n -state IDPDA is represented by an IDPDA with 2(O((m+n)2)) states. This paper presents more efficient constructions for the Kleene star and for the reversal, which yield 2(Theta(n log n)) states, as well as an m2(Theta(n log n))-state construction for the concatenation. These constructions are optimal up to a factor in the exponent, due to the close lower bounds previously established by Piao and Salomaa (2009) [27]. (C) 2017 Elsevier Inc. All rights reserved.