Buchfuhrer, David and Umans, Christopher (2008) The Complexity of Boolean Formula Minimization. In: Automata, Languages and Programming. Lecture Notes in Computer Science. No.5125. Springer , Berlin, pp. 24-35. ISBN 978-3-540-70574-1. https://resolver.caltech.edu/CaltechAUTHORS:20191112-131623581
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Abstract
The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be Σ^P₂-complete and indeed appears as an open problem in Garey and Johnson [GJ79]. The depth-2 variant was only shown to be Σ^P₂-complete in 1998 [Uma98], and even resolving the complexity of the depth-3 version has been mentioned as a challenging open problem. We prove that the depth-k version is Σ^P₂-complete under Turing reductions for all k ≥ 3. We also settle the complexity of the original, unbounded depth Minimum Equivalent Expression problem, by showing that it too is Σ^P₂-complete under Turing reductions.
Item Type: | Book Section | ||||||||||||
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Additional Information: | © 2008 Springer-Verlag Berlin Heidelberg. Supported by NSF CCF-0346991 and BSF 2004329. Supported by NSF CCF-0346991, BSF 2004329, a Sloan Research Fellowship, and an Okawa Foundation research grant. | ||||||||||||
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Subject Keywords: | Positive Instance; Boolean Formula; Negative Instance; Boolean Circuit; Equivalent Formula | ||||||||||||
Series Name: | Lecture Notes in Computer Science | ||||||||||||
Issue or Number: | 5125 | ||||||||||||
DOI: | 10.1007/978-3-540-70575-8_3 | ||||||||||||
Record Number: | CaltechAUTHORS:20191112-131623581 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20191112-131623581 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 99813 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Tony Diaz | ||||||||||||
Deposited On: | 12 Nov 2019 22:46 | ||||||||||||
Last Modified: | 16 Nov 2021 17:49 |
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