A lower bound on CNF encodings of the at-most-one constraint
نویسندگان
چکیده
منابع مشابه
A Lower Bound on CNF Encodings of the At-Most-One Constraint
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 esp...
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In this paper, we study how to encode the at-most-one (AMO) constraint in conjunctive normal form (CNF). The AMO constraint means that at most one out of n propositional variables is allowed to be true. We present a new AMO encoding that improves on the existing one. The logarithmic bitwise AMO encoding by Frisch et al. requires log n auxiliary variables and n log n clauses. Sinz’s sequential A...
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Motivated by the performance improvements made to SAT solvers in recent years, a number of different encodings of constraints into SAT have been proposed. Concrete examples are the different SAT encodings for ≤ 1 (x1, . . . , xn) constraints. The most widely used encoding is known as the pairwise encoding, which is quadratic in the number of variables in the constraint. Alternative encodings ar...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2019
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2018.09.003