TY - GEN

T1 - Trade-offs between time and memory in a tighter model of CDCL SAT solvers

AU - Elffers, Jan

AU - Johannsen, Jan

AU - Lauria, Massimo

AU - Magnard, Thomas

AU - Nordström, Jakob

AU - Vinyals, Marc

PY - 2016

Y1 - 2016

N2 - 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 forgot- ten, 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 cap- tures 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 with- out 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.

AB - 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 forgot- ten, 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 cap- tures 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 with- out 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.

UR - http://www.scopus.com/inward/record.url?scp=84977484096&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-40970-2_11

DO - 10.1007/978-3-319-40970-2_11

M3 - Article in proceedings

AN - SCOPUS:84977484096

SN - 9783319409696

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 160

EP - 176

BT - Theory and Applications of Satisfiability Testing – SAT 2016 - 19th International Conference, Proceedings

A2 - Le Berre, Daniel

A2 - Creignou, Nadia

PB - Springer Verlag,

T2 - 19th International Conference on Theory and Applications of Satisfiability Testing, SAT 2016

Y2 - 5 July 2016 through 8 July 2016

ER -