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The Complexity of Boolean Formula Minimization

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.

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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.

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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.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)2004329
Alfred P. Sloan FoundationUNSPECIFIED
Okawa FoundationUNSPECIFIED
Subject Keywords:Positive Instance; Boolean Formula; Negative Instance; Boolean Circuit; Equivalent Formula
Series Name:Lecture Notes in Computer Science
Issue or Number:5125
Record Number:CaltechAUTHORS:20191112-131623581
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99813
Deposited By: Tony Diaz
Deposited On:12 Nov 2019 22:46
Last Modified:16 Nov 2021 17:49

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