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Revision #3 to TR12-096 | 9th January 2013 13:15

Bounded-width QBF is PSPACE-complete

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Revision #3
Authors: Albert Atserias, Sergi Oliva
Accepted on: 9th January 2013 13:15
Downloads: 725
Keywords: 


Abstract:

Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.



Changes to previous version:

Fixed some typos.


Revision #2 to TR12-096 | 19th September 2012 15:41

Bounded-width QBF is PSPACE-complete





Revision #2
Authors: Albert Atserias, Sergi Oliva
Accepted on: 19th September 2012 15:41
Downloads: 733
Keywords: 


Abstract:

Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi [LICS 2006] that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.


Revision #1 to TR12-096 | 26th July 2012 19:08

Bounded-width QBF is PSPACE-complete





Revision #1
Authors: Albert Atserias, Sergi Oliva
Accepted on: 26th July 2012 19:08
Downloads: 665
Keywords: 


Abstract:

Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.



Changes to previous version:

Minor rewriting of introduction.


Paper:

TR12-096 | 17th July 2012 23:18

Bounded-width QBF is PSPACE-complete





TR12-096
Authors: Albert Atserias, Sergi Oliva
Publication: 26th July 2012 19:02
Downloads: 1230
Keywords: 


Abstract:

Tree-width is a well-studied parameter of structures that measures their similarity to a tree. Many important NP-complete problems, such as Boolean satisfiability (SAT), are tractable on bounded tree-width instances. In this paper we focus on the canonical PSPACE-complete problem QBF, the fully-quantified version of SAT. It was shown by Pan and Vardi that this problem is PSPACE-complete even for formulas whose tree-width grows extremely slowly. Vardi also posed the question of whether the problem is tractable when restricted to instances of bounded tree-width. We answer this question by showing that QBF on instances with constant tree-width is PSPACE-complete.



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