Related papers: On CNF Conversion for SAT and SMT Enumeration

Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…

In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…

We consider the well-studied partial sums problem in succint space where one is to maintain an array of n k-bit integers subject to updates such that partial sums queries can be efficiently answered. We present two succint versions of the…

Parity reasoning is challenging for Conflict-Driven Clause Learning (CDCL) SAT solvers. This has been observed even for simple formulas encoding two contradictory parity constraints with different variable orders (Chew and Heule 2020). We…

We describe an algorithm to solve the problem of Boolean CNF-Satisfiability when the input formula is chosen randomly. We build upon the algorithms of Sch{\"{o}}ning 1999 and Dantsin et al.~in 2002. The Sch{\"{o}}ning algorithm works by…

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…

Convolutional neural networks (CNNs) have a large number of variables and hence suffer from a complexity problem for their implementation. Different methods and techniques have developed to alleviate the problem of CNN's complexity, such as…

The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiability algorithms, and average-case hardness over this…

The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most…

This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…

Modern conflict-driven clause learning (CDCL) SAT solvers are very good in solving conjunctive normal form (CNF) formulas. However, some application problems involve lots of parity (xor) constraints which are not necessarily efficiently…

Open questions with respect to the computational complexity of linear CNF formulas in connection with regularity and uniformity are addressed. In particular it is proven that any l-regular monotone CNF formula is XSAT-unsatisfiable if its…

Supervised Fine-Tuning (SFT) is widely used for task-specific adaptation, yet recent work shows it systematically undermines reasoning generalization. We argue the root cause is not memorization itself, but its target: vanilla SFT drives…

Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F . Model counting is a fundamental but hard problem in computer science with varied applications. Recent…

While prior work established a verifier-based polynomial-time framework for NP, explicit deterministic machines for concrete NP-complete problems have remained elusive. In this paper, we construct fully specified deterministic Turing…

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…

Feature models are commonly used to specify the valid configurations of a product line. In industry, feature models are often complex due to a large number of features and constraints. Thus, a multitude of automated analyses have been…

Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical…

This paper describes learning in a compiler for algorithms solving classes of the logic minimization problem MINSAT, where the underlying propositional formula is in conjunctive normal form (CNF) and where costs are associated with the…

We study the complexity of SAT($\Gamma$) problems for potentially infinite languages $\Gamma$ closed under variable negation (sign-symmetric languages). Via an algebraic connection, this reduces to the study of restricted partial…