From Backtracking to Chaff
نویسندگان
چکیده
Modern Chaff-like SAT solvers enhance plain backtracking (DLL) by Conflict-Driven Learning (CDL), including 1UIP-based Conflict-Directed Backjumping (CDB), Non-Chronological Backtracking (NCB), and 1UIP-based Conflict-Clause Recording (CCR). We show how to add these enhancements step-by-step to plain DLL to derive Chaff’s Conflict-Driven Learning algorithm, separately and independently of BCP, and without reference to implication graphs. We demonstrate that DLL with 1UIP-based CDB, DLL with NCB, plain DLL and tree-like resolution are equal in inference power; and provide a family of formulas linearly separating DLL from DLL with BCP. We demonstrate that a general resolution refutation with t shared subtrees can be simulated by DLL with CCR, making at most t restarts; and propose a new technique, called Conflict Non-Determinism (CND), which makes DLL, enhanced with CCR but without restarts, equal in power to general resolution.
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