The paper introduces a hybrid framework for solving Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT‑NRA). It presents a new two‑dimensional cell‑jump move, called 2D‑cell‑jump, that generalizes the existing cell‑jump operation by allowing search over any chosen plane. Building on this, the authors develop an extended local search framework, 2D‑LS, and combine it with MCSAT and OpenCAD to form a hybrid solver that improves search efficiency through information exchange, as shown by experimental results.
arXiv:2606. 06656v1 Announce Type: new Abstract: We study parallel Continuous Local Search (CLS) as a solution approach for Boolean satisfiability problems with symmetric pseudo-Boolean (PB) constraints.
arXiv:2606. 31878v1 Announce Type: cross Abstract: We investigate two approaches for extending CEGAR-tableaux with SAT-shortcuts using a previously known approach called RECAR but also a totally new approach using the modal resolution theorem prover KSP as an oracle.
arXiv:2608. 15143v1 Announce Type: new Abstract: Constraint solving is a declarative approach for solving combinatorial satisfaction and optimization problems.
The paper presents an exact 93‑move solution to a nonlocal crystal‑exchange puzzle on an 11×11 board, where a command swaps the player with the nearest crystal in a chosen row or column. The authors prove that no shorter solution exists by performing a cost‑bounded breadth‑first search that explores over 1.8 billion states, using a compressed core abstraction and several pruning conditions. The study includes a detailed description of the reductions, pruning rules, storage scheme, and provides source code, execution logs, and a reproduction driver.
GradSAT is a new framework that improves satisfiability solving for Quantifier-Free Floating-Point formulas by treating each SMT clause as an independent multi‑task learning problem. It uses dynamic gradient normalization (GradNorm) to balance gradient magnitudes across clauses, preventing a few difficult clauses from dominating the optimization trajectory. The approach combines a GPU‑accelerated PyTorch backend for continuous relaxation with a precise local search engine, yielding a robust, highly parallelizable solver.
The paper introduces the Minimum Span Antibandwidth and Cyclic Antibandwidth Labeling (MSABL/MSCABL) problems, which fix a minimum (cyclic) distance between labels of adjacent vertices and aim to minimize the overall label span. A unified Boolean Satisfiability (SAT) framework is developed, formulating the problems as a sequence of decision problems and exploiting monotonicity to accelerate search. Two SAT solving strategies—parallel and incremental—are evaluated on benchmark instances, showing that SAT-based approaches are highly competitive with commercial solvers, especially for MSCABL.
arXiv:2606. 06641v1 Announce Type: new Abstract: We present Accelerated Fourier SAT (AFSAT), a GPU-accelerated solver for pseudo-Boolean satisfiability based on continuous local search (CLS).
The paper introduces the Minimum Span Antibandwidth and Cyclic Antibandwidth Labeling (MSABL/MSCABL) problems, which fix a minimum (cyclic) distance between adjacent vertex labels and aim to minimize the overall label span. A unified Boolean Satisfiability (SAT) framework is developed, formulating the problems as a sequence of decision problems and exploiting monotonicity to accelerate search. Two SAT solving strategies—parallel and incremental—are evaluated on benchmark instances from the Harwell‑Boeing Sparse Matrix Collection and compared with commercial solvers, showing that SAT-based approaches are highly competitive, with the parallel method best for MSCABL and the incremental method best for MSABL.
The paper introduces a method for numerical Totally-Ordered HTN (TOHTN) planning by extending standard SAT-based encodings with SMT to handle numeric fluents. It also presents a new benchmark suite for evaluating numerical TOHTN planning, providing a common basis for future research. Experimental results demonstrate that this straightforward encoding serves as a competitive baseline for the field.
arXiv:2607. 23393v1 Announce Type: new Abstract: Existing exact methods for 4-connected grid pathfinding reduce online search, but often either retain fine-grained search states or require substantial preprocessing.
arXiv:2507. 22876v2 Announce Type: replace Abstract: The Satisfiability problem (SAT) is fundamental in computational complexity theory and has a wide range of industrial applications.
arXiv:2606. 07047v1 Announce Type: new Abstract: Heuristics play a central role in the performance of bidirectional search algorithms, which commonly rely on two main classes.