A Lower Bound on CNF Encodings of the At-Most-One Constraint

0478486 - ÚI 2018 RIV CH eng C - Conference Paper (international conference)
Kučera, P. - Savický, Petr - Vorel, V.
A Lower Bound on CNF Encodings of the At-Most-One Constraint.
Theory and Applications of Satisfiability Testing - SAT 2017. Cham: Springer, 2017 - (Gaspers, S.; Walsh, T.), s. 412-428. Lecture Notes in Computer Science, 10491. ISBN 978-3-319-66262-6. ISSN 0302-9743.
[SAT 2017. International Conference on Theory and Applications of Satisfiability Testing /20./. Melbourne (AU), 28.08.2017-01.09.2017]
R&D Projects: GA ČR GBP202/12/G061
Grant - others:GA ČR(CZ) GA15-15511S
Institutional support: RVO:67985807
Keywords : Knowledge compilation * Cardinality constraint * At most one constraint * Propagation complete encoding
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Constraint ”at most one” is a basic cardinality constraint which requires that at most one of its n boolean inputs is set to 1. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we investigate its CNF encodings suitable for this purpose. An encoding differs from a CNF representation of a function in that it can use auxiliary variables. We are especially interested in propagation complete encodings which have the property that unit propagation is strong enough to enforce consistency on input variables. We show a lower bound on the number of clauses in any propagation complete encoding of the ”at most one” constraint. The lower bound almost matches the size of the best known encodings. We also study an important case of 2-CNF encodings where we show a slightly better lower bound. The lower bound holds also for a related ”exactly one” constraint.
Permanent Link: http://hdl.handle.net/11104/0274603