Backing Backtracking

Combining Conflict-Driven Clause Learning and Chronological Backtracking for Propositional Model Counting

“…We clarify these concepts by means of an example taken from [21]. Consider the trail I on the left hand side of Note that since the assignment order is preserved, the trail still contains one out-of-order literal, namely 3.…”

“…To define more precisely the concepts introduced in [23], in [21] we provided a formalization and formal proof and generalization of the procedure. Our goal was to understand which invariants are crucial and which are redundant and to empirically confirm the effectiveness of chronological backtracking.…”

“…In [21], we characterized five invariants, three of which are violated by chronological backtracking. Still the procedure remains correct and we proved empirically that always executing chronological backtracking in combination with CDCL does not degrade significantly solver performance confirming the suitability of chronological backtracking for model counting.…”

“…Our contribution. In this work we extend our framework [21] to serve propositional model counting and provide a formal proof of its correctness. We present a counting algorithm based on model enumeration.…”

“…First, we extend the original calculus [21] by one rule, to capture the situation where a model is found. Second, the states now include all the (partial) models found at any point in time of the search.…”