Marijn J. H. Heule

Inprocessing rules

Decision procedures for Boolean satisfiability (SAT), especially modern conflict-driven clause learning (CDCL) solvers, act routinely as core solving engines in various real-world applications. Preprocessing, i.e., applying formula rewriting/simplification rules to the input formula before the actual search for satisfiability, has become an essential part of the SAT solving tool chain. Further, some of the strongest SAT solvers today add more reasoning to search by interleaving formula simplification and CDCL search. Such inprocessing SAT solvers witness the fact that implementing additional deduction rules in CDCL solvers leverages the efficiency of state-of-the-art SAT solving further. In this paper we establish formal underpinnings of inprocessing SAT solving via an abstract inprocessing framework that covers a wide range of modern SAT solving techniques.

Blocked clause elimination

Boolean satisfiability (SAT) and its extensions are becoming a core technology for the analysis of systems. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantagecompared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. In this work we study the effect of a CNF-level simplification technique called blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNFs resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. Experimentally, we show that by applying BCE in preprocessing, further formula reduction and faster solving can be achieved, giving promise for applying BCE to speed up solvers.

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 partitions a problem into many thousands (or millions) of cubes using lookahead techniques. Afterwards, a conflict-driven solver tackles the problem, using the cubes to guide the search. On several hard competition benchmarks, our hybrid approach outperforms both lookahead and conflict-driven solvers. Moreover, because cube-and-conquer is natural to parallelize, it is a competitive alternative for solving SAT problems in parallel.

March_eq: implementing additional reasoning into an efficient look-ahead SAT solver

This paper discusses several techniques to make the look- ahead architecture for satisfiability (Sat) solvers more competitive. Our contribution consists of reduction of the computational costs to perform look-ahead and a cheap integration of both equivalence reasoning and local learning. Most proposed techniques are illustrated with experimental results of their implementation in our solver march_eq.

Clause elimination procedures for CNF formulas

We develop and analyze clause elimination procedures, a specific family of simplification techniques for conjunctive normal form (CNF) formulas. Extending known procedures such as tautology, subsumption, and blocked clause elimination, we introduce novel elimination procedures based on hidden and asymmetric variants of these techniques. We analyze the resulting nine (including five new) clause elimination procedures from various perspectives: size reduction, BCP-preservance, confluence, and logical equivalence. For the variants not preserving logical equivalence, we show how to reconstruct solutions to original CNFs from satisfying assignments to simplified CNFs. We also identify a clause elimination procedure that does a transitive reduction of the binary implication graph underlying any CNF formula purely on the CNF level.

Solving 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 =

DRAT-trim: Efficient Checking and Trimming Using Expressive Clausal Proofs

\{1, 2, ...\}

Automated reencoding of boolean formulas

of natural numbers be divided into two parts, such that no part contains a triple

Trimming while checking clausal proofs

(a,b,c)

Simulating Circuit-Level Simplifications on CNF

with