State complexity of operations on input-driven pushdown automata

Authors:
Alexander Okhotin;Kai Salomaa
Affiliations:
Department of Mathematics, University of Turku, Turku, Finland and Academy of Finland;School of Computing, Queen's University, Kingston, Ontario, Canada
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

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Abstract

The 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 2O(n2) states, while concatenation of an m-state and an n-state IDPDA is represented by an IDPDA with 2O((m+n)2) states. This paper presents more efficient constructions for the reversal and for the Kleene star, which yield 2Θ(n log n) states, as well as an m2Θ(n log n)-state construction for the concatenation. These constructions are optimal due to the previously known matching lower bounds.