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Journal of Logic and Computation 2005 15(4):551-557; doi:10.1093/logcom/exi033
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Vol. 15 No. 4, © The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Approximating Succinct MaxSat

Christian Schallhart1 and Luca Trevisan2

1 Institut für Informatik (I7) TU München, Boltzmannstraße 3, D-85748 Garching bei München, Germany. Email: schallha{at}in.tum.de, 2 University of California at Berkeley, Computer Science Division, 615 Soda Hall, Berkeley, CA 94720-1776, USA. Email: luca{at}eecs.berkeley.edu

We study the approximability of the version of MAXSAT where exponentially large instances are succinctly represented using circuits. First, we prove that the NP-hardness for approximating MAXSAT can be lifted to a corresponding NEXP-hardness for approximating circuit-succinct MAXSAT for some constant performance ratio. Second, we consider the approximability of circuit-succinct MAXSAT with respect to lower complexity classes: in particular, we prove that computing (2 – {epsilon})-approximate solutions for circuit-succinct MAXSAT is at least as hard as inverting one-way permutations. On the other hand, a simple randomized approximation algorithm computes a (2 + {epsilon})-approximate solution with high probability. Recall that the standard (not succinctly represented) version of the MAXSAT problem is approximable to within a 0.78 factor and that the MAX3SAT problem is approximable to within a 7/8 factor.

Keywords: Approximation, succinctness, SAT

Received 29 May 2005.


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