By South Africa) African Electrical Technology Conference (5th : 1999 : Cape Town
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Extra info for Africon '99: 5th Africon Conference in Africa, Electrotechnological Services for Africa;28 September - 1 October 1999 Hosted by Cape Technikon Cape Town, South afr
A Partial Max-SAT instance is a CNF formula in which some clauses are relaxable or soft and the rest are non-relaxable or hard. Solving a Partial MaxSAT instance amounts to ﬁnd an assignment that satisﬁes all the hard clauses and the maximum number of soft clauses. Research partially supported by projects TIN2004-07933-C03-03 and TIN200615662-C02-02 funded by the Ministerio de Educaci´ on y Ciencia. J. A. ): SAT 2007, LNCS 4501, pp. 28–40, 2007. c Springer-Verlag Berlin Heidelberg 2007 Partial Max-SAT Solvers with Clause Learning 29 Let us illustrate with an example the expressive power of Partial Max-SAT.
If its weight is , it is clear that the formula does not have any model. If its weight is w, the cost of any assignment will include that weight, so w is an obvious lower bound of the formula optimal cost. Weighted empty clauses and their interpretation in terms of lower bounds will become relevant in Section 4. Mandatory clauses of size 1 (namely, (l, )) are called facts. When a formula contains a fact (l, ), it can be simplified by removing all clauses containing l and removing l¯ from all the clauses where it appears.
Heras and J. Larrosa. New inference rules for eﬃcient Max-SAT solving. In Proceedings of the National Conference on Artificial Intelligence, AAAI-2006, Boston/MA, USA, pages 68–73, 2006. 12. F. Heras, J. Larrosa, and A. Oliveras. Minimaxsat: A new weighted Max-SAT solver. In Proceedings of the 10th International Conference on Theory and Applications of Satisfiability Testing, SAT-2007, Lisbon, Portugal, 2007. 13. R. G. Jeroslow and J. Wang. Solving propositional satisﬁability problems. Annals of Mathematics and Artificial Intelligence, 1:167–187, 1990.