Abstract
An autarky for a formula in propositional logic is a truth assignment that satisfies every clause it touches, i.e., every clause for which the autarky assigns at least one variable. In this paper, we present how conditional autarkies, a generalization of autarkies, give rise to novel preprocessing techniques for SAT solving. We show that conditional autarkies correspond to a new type of redundant clauses, termed globally-blocked clauses, and that the elimination of these clauses can simulate existing circuit-simplification techniques on the CNF level.
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Acknowledgment
This work has been supported by the National Science Foundation under grant CCF-1618574 and by the Austrian Science Fund (FWF) under project W1255 (LogiCS) and S11409-N23 (RiSE).
We want to thank Oliver Kullmann, who explained to the second author an (as far as we know unpublished) algorithm to compute the maximal autarky of a total assignment, which is a special case of \(\mathsf {LeastConditionalPart}\) in Fig. 1.
This work was triggered by Gianpiero Cabodi who asked the last author whether there is a CNF level version of unique sensitization as explained in Sect. 3 with potential applications in SAT-based model checking.
We would finally also like to thank the organizers of ATVA’19 for inviting the last author to present these ideas as invited talk and include this invited paper in the proceedings.
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Kiesl, B., Heule, M.J.H., Biere, A. (2019). Truth Assignments as Conditional Autarkies. In: Chen, YF., Cheng, CH., Esparza, J. (eds) Automated Technology for Verification and Analysis. ATVA 2019. Lecture Notes in Computer Science(), vol 11781. Springer, Cham. https://doi.org/10.1007/978-3-030-31784-3_3
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DOI: https://doi.org/10.1007/978-3-030-31784-3_3
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