Trade-offs Between Time and Memory in a Tighter Model of CDCL SAT Solvers
A long line of research has studied the power of conflict-driven clause learning (CDCL) and how it compares to the resolution proof system in which it searches for proofs. It has been shown that CDCL can polynomially simulate resolution even with an adversarially chosen learning scheme as long as it is asserting. However, the simulation only works under the assumption that no learned clauses are ever forgotten, and the polynomial blow-up is significant. Moreover, the simulation requires very frequent restarts, whereas the power of CDCL with less frequent or entirely without restarts remains poorly understood. With a view towards obtaining results with tighter relations between CDCL and resolution, we introduce a more fine-grained model of CDCL that captures not only time but also memory usage and number of restarts. We show how previously established strong size-space trade-offs for resolution can be transformed into equally strong trade-offs between time and memory usage for CDCL, where the upper bounds hold for CDCL without any restarts using the standard 1UIP clause learning scheme, and the (in some cases tightly matching) lower bounds hold for arbitrarily frequent restarts and arbitrary clause learning schemes.
KeywordsMemory Usage Proof System Unit Clause General Resolution Conflict Analysis
We are grateful to the anonymous SAT conference reviewers for detailed comments that helped improve the exposition in this paper.
The third author performed this work while at KTH Royal Institute of Technology, and most of the work of the second and fourth author was done while visiting KTH. The first, third, fifth, and sixth author were funded by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013) / ERC grant agreement no. 279611 as well as by Swedish Research Council grant 621-2012-5645. The third author was also supported by the European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme/ERC grant agreement no. 648276.
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