Abstract
AbstractThe family of deterministic input-driven pushdown automata (IDPDA; a.k.a. visibly pushdown automata, a.k.a. nested word automata) is known to be closed under reversal, concatenation and Kleene star. As shown by Alur and Madhusudan (``Visibly pushdown languages'', STOC 2004), the reversal and the Kleene star of an n-state IDPDA can be represented by an IDPDA with \(2^{O(n^2)}\) 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 reversal and for the Kleene star, which yield 2Θ(n logn) states, as well as an m 2Θ(n logn)-state construction for the concatenation. These constructions are optimal due to the previously known matching lower bounds.
Published Version
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