Improving SAT and pseudo-boolean solving technology
(English) The Boolean satisfiability (SAT) problem has seen remarkable progress, from early DPLL and resolution methods to the modern Conflict-Driven Clause Learning (CDCL) paradigm. Nevertheless, significant challenges remain. Theoretically "simple" yet structurally complex problems, such...
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| Format: | doctoral thesis |
| Publication Date: | 2026 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/456957 |
| Online Access: | https://hdl.handle.net/2117/456957 https://dx.doi.org/10.5821/dissertation-2117-456957 |
| Access Level: | Open access |
| Keyword: | SAT Pseudo-Boolean Optimization CDCL Unit Propagation Conflict Analysis. Optimización Pseudo-Booleana Propagación Unitaria Análisis de Conflictos Optimizació Pseudo-Booleana Propagació Unitària Anàlisi de Conflictes 004 - Informàtica Àrees temàtiques de la UPC::Informàtica |
| Summary: | (English) The Boolean satisfiability (SAT) problem has seen remarkable progress, from early DPLL and resolution methods to the modern Conflict-Driven Clause Learning (CDCL) paradigm. Nevertheless, significant challenges remain. Theoretically "simple" yet structurally complex problems, such as the pigeonhole principle, continue to challenge state-of-the-art SAT solvers, revealing inherent limitations in core algorithms like CDCL. Although CDCL-based Pseudo-Boolean (PB) solving extends SAT with 0-1 linear arithmetic constraints—enabling more natural modeling and offering exponential speedups in theory—its added complexity introduces computational bottlenecks in propagation, conflict analysis, and optimization. These challenges underscore the need for deeper algorithmic insights and innovative techniques to advance SAT and PB solver performance. This thesis addresses these gaps by advancing the core algorithms and implementation techniques underlying modern SAT and PB solvers. It is structured in two parts: • Part I: SAT Solving – We analyze the limitations of CDCL through both theoretical and practical lenses. The contributions are: (i) new insights from analyzing multiple conflicts, aimed at identifying opportunities to enhance CDCL or understanding the fundamental reasons for the failure of this particular idea; (ii) an empirical study on the equivalence between CDCL solvers and resolution, examining how solvers reproduce unsatisfiability proofs and how decision heuristics and resolution proofs interact. • Part II: Pseudo-Boolean Solving – We introduce optimizations in unit propagation and conflict analysis. Propagation is accelerated through a carefully engineered hybrid technique, while enhanced conflict analysis produces some stronger constraints for more effective search pruning. Beyond performance gains, this work offers profound insights into Boolean constraint reasoning, bridging theoretical gaps and opening new research avenues in SAT, PB, and beyond. |
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