Related papers: MatSat: a matrix-based differentiable SAT solver
Today's propositional satisfiability (SAT) solvers are extremely powerful and can be used as an efficient back-end for solving NP-complete problems. However, many fundamental problems in knowledge representation and reasoning are located at…
We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown,…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
SAT solvers are indispensable in formal verification for hardware and software with many important applications. CDCL is the most widely used framework for modern SAT solvers, and restart is an essential technique of CDCL. When restarting,…
A variant of the well-known Shortest Path Problem is studied in this paper, where pairs of conflicting arcs are provided, and for each conflicting pair a penalty is paid once neither or both of the arcs are selected. This configures a set…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
When creating benchmarks for SAT solvers, we need SAT instances that are easy to build but hard to solve. A recent development in the search for such methods has led to the Balanced SAT algorithm, which can create k-SAT instances with m…
The 3-Satisfiability Problem (3-SAT) is a demanding combinatorial problem, of central importance among the non-deterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence and logistics. Even…
In this paper, we address the problem of enumerating all models of a Boolean formula in conjunctive normal form (CNF). We propose an extension of CDCL-based SAT solvers to deal with this fundamental problem. Then, we provide an experimental…
The CDCL algorithm is the leading solution adopted by state-of-the-art solvers for SAT, SMT, ASP, and others. Experiments show that the performance of CDCL solvers can be significantly boosted by embedding domain-specific heuristics,…
We give a first account of our new parallel SAT solver Gimsatul. Its key feature is to share clauses physically in memory instead of copying them, which is the method of other state-of-the-art multi-threaded SAT solvers to exchange clauses…
Reconfiguration aims at recovering a system from a fault by automatically adapting the system configuration, such that the system goal can be reached again. Classical approaches typically use a set of pre-defined faults for which…
We propose a resource-constrained heuristic for instances of Max-SAT that iteratively decomposes a larger problem into smaller subcomponents that can be solved by optimized solvers and hardware. The unconstrained outer loop maintains the…
One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as…
Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
We analyze rank decompositions of the $3\times 3$ matrix multiplication tensor over $\mathbb{Z}/2\mathbb{Z}$. We restrict our attention to decompositions of rank $\le 21$, as only those decompositions will yield an asymptotically faster…
Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT).…
We introduce the problem of finding a satisfying assignment to a CNF formula that must further belong to a prescribed input subspace. Equivalent formulations of the problem include finding a point outside a union of subspaces (the…