TY - GEN

T1 - Linear satisfiability preserving assignments

AU - Kimura, Kei

AU - Makino, Kazuhisa

N1 - Funding Information:
The authors thank Dr. Yasushi Kawase for fruitful discussion on Theorem 5. The first author is supported by JSPS KAKENHI Grant Number JP15H06286. The second author is supported by JSPS KAKENHI Grant Number JP24106002, JP25280004, JP26280001, and JST CREST Grant Number JPMJCR1402, Japan.
Publisher Copyright:
© 2018 International Joint Conferences on Artificial Intelligence.All right reserved.

PY - 2018

Y1 - 2018

N2 - In this paper, we study several classes of satisfiability preserving assignments to the constraint satisfaction problem. In particular, we consider fixable, autark and satisfying assignments. Since it is in general NP-hard to find a nontrivial (i.e., nonempty) satisfiability preserving assignment, we introduce linear satisfiability preserving assignments, which are defined by polyhedral cones in an associated vector space. The vector space is obtained by the identification, introduced by Kullmann, of assignments with real vectors. We consider arbitrary polyhedral cones, where only restricted classes of cones for autark assignments are considered in the literature. We reveal that cones in certain classes are maximal as a convex subset of the set of the associated vectors, which can be regarded as extensions of Kullmann's results for autark assignments of CNFs. As algorithmic results, we present a pseudo-polynomial time algorithm that computes a linear fixable assignment for a given integer linear system, which implies the well known pseudo-polynomial solvability for integer linear systems such as two-variable-per-inequality, Horn and q-Horn systems.

AB - In this paper, we study several classes of satisfiability preserving assignments to the constraint satisfaction problem. In particular, we consider fixable, autark and satisfying assignments. Since it is in general NP-hard to find a nontrivial (i.e., nonempty) satisfiability preserving assignment, we introduce linear satisfiability preserving assignments, which are defined by polyhedral cones in an associated vector space. The vector space is obtained by the identification, introduced by Kullmann, of assignments with real vectors. We consider arbitrary polyhedral cones, where only restricted classes of cones for autark assignments are considered in the literature. We reveal that cones in certain classes are maximal as a convex subset of the set of the associated vectors, which can be regarded as extensions of Kullmann's results for autark assignments of CNFs. As algorithmic results, we present a pseudo-polynomial time algorithm that computes a linear fixable assignment for a given integer linear system, which implies the well known pseudo-polynomial solvability for integer linear systems such as two-variable-per-inequality, Horn and q-Horn systems.

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M3 - Conference contribution

AN - SCOPUS:85055685940

T3 - IJCAI International Joint Conference on Artificial Intelligence

SP - 5622

EP - 5626

BT - Proceedings of the 27th International Joint Conference on Artificial Intelligence, IJCAI 2018

A2 - Lang, Jerome

PB - International Joint Conferences on Artificial Intelligence

T2 - 27th International Joint Conference on Artificial Intelligence, IJCAI 2018

Y2 - 13 July 2018 through 19 July 2018

ER -