A1 Refereed original research article in a scientific journal
State Complexity of Operations on Input-Driven Pushdown Automata
Authors: Okhotin A, Salomaa K
Publication year: 2011
Journal: Lecture Notes in Computer Science
Journal name in source: MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE 2011
Journal acronym: LECT NOTES COMPUT SC
Volume: 6907
First page : 485
Last page: 496
Number of pages: 12
ISBN: 978-3-642-22992-3
ISSN: 0302-9743
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 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 reversal and for the Kleene star, 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 due to the previously known matching lower bounds.
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 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 reversal and for the Kleene star, 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 due to the previously known matching lower bounds.
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