An Exponential Separation between Deterministic CDCL and DPLL Solvers

Sahil Samar; Marc Vinyals; Vijay Ganesh

doi:10.4230/lipics.sat.2026.30

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arXiv · 2603.16156

An Exponential Separation between Deterministic CDCL and DPLL Solvers

Sahil Samar·Marc Vinyals·Vijay Ganesh

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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.

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Sahil Samar, Marc Vinyals, Vijay Ganesh. 2026-03-17. An Exponential Separation between Deterministic CDCL and DPLL Solvers. https://doi.org/10.4230/lipics.sat.2026.30

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