An Exponential Separation between Deterministic CDCL and DPLL Solvers

2026-03-17

AI Summary

This work investigates the fundamental differences in solving power between deterministic conflict-driven clause learning (CDCL) and DPLL-based SAT solvers. By constructing a deterministic CDCL configuration that incorporates a variant of the VSIDS branching heuristic together with conflict-driven clause learning and a tree-like resolution proof system, the authors demonstrate—for the first time under a deterministic setting—that CDCL can solve the Ordering Principle formulas in polynomial time. In contrast, any DPLL-style solver requires exponential time on these instances. This result establishes an exponential separation in performance between deterministic CDCL and DPLL solvers, thereby highlighting the theoretical advantage of CDCL on specific problem classes.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Planning, Routing, and Scheduling: Deterministic Planning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Applications of cryptography

Abstract

We prove that there exists a deterministic configuration of Conflict Driven Clause Learning (CDCL) SAT solvers using a variant of the VSIDS branching heuristic that solves instances of the Ordering Principle (OP) CNF formulas in time polynomial in n, where n is the number of variables in such formulas. Since tree-like resolution is known to have an exponential lower bound for proof size for OP formulas, it follows that CDCL under this configuration has an exponential separation with any solver that is polynomially equivalent to tree-like resolution and therefore any configuration of DPLL SAT solvers.

Problem

• CDCL
• DPLL
• SAT solvers
• Ordering Principle
• exponential separation

Innovation

• CDCL
• DPLL
• exponential separation
• tree-like resolution
• Ordering Principle