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Summary: Importance of Variables Semantic in CNF Encoding of Cardinality Constraints
Anbulagan
NICTA & The Australian National University
Canberra, Australia
anbulagan@nicta.com.au
Alban Grastien
NICTA & The Australian National University
Canberra, Australia
alban.grastien@nicta.com.au
Abstract
In the satisfiability domain, it is well-known that a SAT al-
gorithm may solve a problem instance easily and another in-
stance hardly, whilst these two instances are equivalent CNF
encodings of the original problem. Moreover, different algo-
rithms may disagree on which encoding makes the problem
easier to solve. In this paper, we focus on the CNF encoding
of cardinality constraints, which states that exactly k proposi-
tional variables in a given set are assigned to true. We demon-
strate the importance of the semantics of the SAT variables in
the encoding of this constraint. We implement several vari-
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