BDDs for Pseudo-Boolean Constraints
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hdl:2117/14739
Document typeConference report
Defense date2011
PublisherSpringer Verlag
Rights accessRestricted access - publisher's policy
Abstract
Pseudo-Boolean constraints are omnipresent in practical
applications, and therefore a significant effort has been devoted to the
development of good SAT encoding techniques for these constraints. Several
of these encodings are based on building Binary Decision Diagrams
(BDDs) and translating these into CNF. Indeed, BDD-based encodings
have important advantages, such as sharing the same BDD for representing
many constraints.
Here we first prove that, unless NP = Co-NP, there are Pseudo-
Boolean constraints that admit no variable ordering giving a polynomial
(Reduced, Ordered) BDD. As far as we know, this result is new (in
spite of some misleading information in the literature). It gives several
interesting insights, also relating proof complexity and BDDs.
But, more interestingly for practice, here we also show how to overcome
this theoretical limitation by coefficient decomposition. This allows
us to give the first polynomial arc-consistent BDD-based encoding for
Pseudo-Boolean constraints.
CitationAbío, I. [et al.]. BDDs for Pseudo-Boolean Constraints. A: International Conference on Theory and Applications of Satisfiability Testing. "SAT 2011 - Theory and Applications of Satisfiability Testing". Ann Arbor, MI, USA: Springer Verlag, 2011, p. 61-75.
ISBN978-3-642-21580-3
Publisher versionhttp://www.springerlink.com/content/l76mt89727133500/
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