Chronological Backtracking

Nadel, Alexander; Ryvchin, Vadim

doi:10.1007/978-3-319-94144-8_7

Cited by 42 publications

(35 citation statements)

References 8 publications

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“…The results for combining chronological backtracking with CDCL presented in [23] and its potential for propositional model counting conjectured in [21] provided the main motivation for our work. We have presented a formal calculus for propositional model counting based on these ideas and provided a formal proof of its correctness.…”

Section: Resultsmentioning

confidence: 99%

“…This is not the case in [23] anymore. Assume the formula under consideration evaluates to false under the current assignment.…”

Section: Introductionmentioning

confidence: 87%

“…Combining CDCL and chronological backtracking. A partial answer to this question was provided in [23]. In this paper, chronological backtracking was enabled under certain conditions violating invariants considered crucial to CDCL.…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Möhle¹,

Biere²

EPiC Series in Computing

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In propositional model counting, also named #SAT, the search space needs to be explored exhaustively, in contrast to SAT, where the task is to determine whether a propositional formula is satisfiable. While state-of-the-art SAT solvers are based on non- chronological backtracking, it has also been shown that backtracking chronologically does not significantly degrade solver performance. Hence investigating the combination of chronological backtracking with conflict-driven clause learning (CDCL) for #SAT seems evident. We present a calculus for #SAT combining chronological backtracking with CDCL and provide a formal proof of its correctness.

show abstract

Section: Resultsmentioning

confidence: 99%

“…This is not the case in [23] anymore. Assume the formula under consideration evaluates to false under the current assignment.…”

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Möhle¹,

Biere²

EPiC Series in Computing

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show abstract

“…Finally, a recent result in [17] shows that the non-chronological backtracking of a CDCL solver might be harmful in some SAT instances. We believe that some of the performance gains we observe in the lookahead implementation are due to a similar phenomenon in SMT where the solver backtracks too much during its search.…”

Section: Related Workmentioning

confidence: 99%

Lookahead-Based SMT Solving

Hyvärinen

Marescotti

Sadigova

et al.

EPiC Series in Computing

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The lookahead approach for binary-tree-based search in constraint solving favors branching that provide the lowest upper bound for the remaining search space. The approach has recently been applied in instance partitioning in divide-and-conquer-based parallelization, but in general its connection to modern, clause-learning solvers is poorly understood. We show two ways of combining lookahead approach with a modern DPLL(T)-based SMT solver fully profiting from theory propagation, clause learning, and restarts. Our thoroughly tested prototype implementation is surprisingly efficient as an independent SMT solver on certain instances, in particular when applied to a non-convex theory, where the lookahead-based implementation solves 40% more unsatisfiable instances compared to the standard implementation.

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Encoding Redundancy for Satisfaction-Driven Clause Learning

Heule

Kiesl

Biere

2019

Tools and Algorithms for the Construction and Analysis of Systems

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Satisfaction-Driven Clause Learning (SDCL) is a recent SAT solving paradigm that aggressively trims the search space of possible truth assignments. To determine if the SAT solver is currently exploring a dispensable part of the search space, SDCL uses the so-called positive reduct of a formula: The positive reduct is an easily solvable propositional formula that is satisfiable if the current assignment of the solver can be safely pruned from the search space. In this paper, we present two novel variants of the positive reduct that allow for even more aggressive pruning. Using one of these variants allows SDCL to solve harder problems, in particular the well-known Tseitin formulas and mutilated chessboard problems. For the first time, we are able to generate and automatically check clausal proofs for large instances of these problems.

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Chronological Backtracking

Cited by 42 publications

References 8 publications

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

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

Lookahead-Based SMT Solving

Encoding Redundancy for Satisfaction-Driven Clause Learning

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