Exploring Conflict Generating Decisions: Initial Results (Extended Abstract)
Bibliographic record
Abstract
Boolean Satisfiability (SAT) is an NP-complete problem, indicating its inherent computational hardness. However, Conflict Driven Clause Learning (CDCL) SAT solvers efficiently tackle large instances in diverse domains. Swift conflict identification is crucial for effective problem-solving, as conflicts lead to the learning of search space pruning clauses, pinpointing the root causes of conflicts and preventing their recurrence. CDCL decision heuristics prioritize variables that participated in recent conflicts, anticipating rapid conflict generation and expediting additional clause learning. In practice, only a fraction of decisions lead to conflicts, yet some decisions may yield multiple conflicts. In this paper, we delve into a detailed study of conflict generating decisions in CDCL, distinguishing between single conflict (sc) decisions, generating only one conflict, and multi-conflict (mc) decisions, producing two or more conflicts. Our empirical analysis characterizes each decision type based on the quality of the learned clauses they produce. Furthermore, our theoretical analysis reveals a crucial distinction: consecutive clauses learned within the same mc decision form a chain of clauses, absent in learned clauses from sc decisions. This leads to the hypothesis that the reasons for conflicts in mc decisions are more closely related than the reasons for conflicts in sc decisions, empirically confirmed with our introduced notion of reason proximity. Finally, we propose score reduction (sr) as a novel decision strategy, reducing the selection priority of certain variables from learned clauses in mc decisions. With four sets of benchmarks, culminating in over 1200 benchmarks, empirical evaluation of sr implemented on top of the SAT competition 2023 winner solver reveals the merit of this new strategy.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".