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Local search characteristics of incomplete SAT procedures

This study explores the characteristics of incomplete SAT procedures, focusing on the Tang-Yi algorithm. It discusses effective engineering methods for finding satisfying assignments and examines the challenges in proving the existence of solutions. The analysis is largely empirical, making it difficult to predict the effects of minor changes. The study also introduces a new local search strategy called SDF, which combines steepest descent and multiplicative clauses re-weighting to overcome local minima.

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Local search characteristics of incomplete SAT procedures

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  1. Local search characteristics of incomplete SAT procedures Tang Yi Based on [1]

  2. Local search methods • Effective engineering methods for finding satisfying assignments • Incomplete and cannot prove if the solution exists • Systematic understanding remains elusive • Analysis largely empirical and hard to predict the effects of a minor change

  3. Measuring local search performance (1) • Depth how many clauses remain unsatisfied as search proceeds by averaging depth over all search steps as an overall summary

  4. Measuring local search performance(2) • Mobility how rapidly a local search moves in search space (while it tries to simultaneously stay deep in the object) by calculating the Hamming distance between variable assignments that are k steps apart and average this quantity over the entire sequence

  5. Measuring local search performance(3) • Coverage how many systematically the search explores the entire space by computing the coverage rate to be (n – max gap) / search steps where max gap is the maximum Hamming distance between unexplored assignment and the nearest evaluated assignment

  6. SDF: a new local search strategy • Two main different components (1) steepest descent in more informative objective function (2) multiplicative clauses re-weighting to move out of local minima and travel to promising new regions • Weighted-score function h(x, w) =

  7. SDF procedure • SDF Flip the variable that leads to the greatest increase in weighted-score function • Re-weight re-weight the unsatisfied clauses and re-normalize the clause weights so that the resulting largest difference is flatten the weight profile of the satisfied clauses by shrinking of the distance towards their common mean

  8. Discussion • Systematically reduce the number of flips • Greater computational overhead per flip

  9. Reference [1]Schuurmans,D. and Southey,F.,Local search characteristics of incomplete SAT procedures, Proceedings of the Seventeenth National Conference on Artificial Intelligence (AAAI-2000),Austin,TX,July 2000.

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