Solving Very Hard Problems: Cube-and-Conquer, a Hybrid SAT Solving Method
نویسندگان
چکیده
A recent success of SAT solving has been the solution of the boolean Pythagorean Triples problem [Heule et al., 2016], delivering the largest proof yet, of 200 terabytes in size. We present this and the underlying paradigm Cube-and-Conquer, a powerful general method to solve big SAT problems, based on integrating the “old” and “new” methods of SAT solving.
منابع مشابه
Cube and Conquer: Guiding CDCL SAT Solvers by Lookaheads
Satisfiability (SAT) is considered as one of the most important core technologies in formal verification and related areas. Even though there is steady progress in improving practical SAT solving, there are limits on scalability of SAT solvers. We address this issue and present a new approach, called cube-and-conquer, targeted at reducing solving time on hard instances. This two-phase approach ...
متن کاملSolving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer
The boolean Pythagorean Triples problem has been a longstanding open problem in Ramsey Theory: Can the set N = {1, 2, . . . } of natural numbers be divided into two parts, such that no part contains a triple (a, b, c) with a + b = c ? A prize for the solution was offered by Ronald Graham over two decades ago. We solve this problem, proving in fact the impossibility, by using the Cube-and-Conque...
متن کاملCompositional Propositional Proofs
Many hard-combinatorial problems have only be solved by SAT solvers in a massively parallel setting. This reduces the trust one has in the final result as errors might occur during parallel SAT solving or during partitioning of the original problem. We present a new framework to produce clausal proofs for cube-and-conquer, arguably the most effective parallel SAT solving paradigm for hard-combi...
متن کاملConcurrent Cube-and-Conquer - (Poster Presentation)
Satisfiability solvers targeting industrial instances are currently almost always based on conflict-driven clause learning (CDCL) [5]. This technique can successfully solve very large instances. Yet on small, hard problems lookahead solvers [3] often perform better by applying much more reasoning in each search node and then recursively splitting the search space until a solution is found. The ...
متن کاملLazy Clause Generation: Combining the Power of SAT and CP (and MIP?) Solving
Finite domain propagation solving, the basis of constraint programming (CP) solvers, allows building very high-level models of problems, and using highly specific inference encapsulated in complex global constraints, as well as programming the search for solutions to take into account problem structure. Boolean satisfiability (SAT) solving allows the construction of a graph of inferences made i...
متن کامل