相关论文: Applying GSAT to Non-Clausal Formulas

For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…

We present a deterministic approximation algorithm to compute logarithm of the number of `good' truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by `good' we mean that violate a small fraction of clauses).…

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 consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding…

This paper provides a technique for evaluating some nonlinear Gaussian sums in closed forms. The evaluation is obtained from the known values of simpler exponential sums.

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…

Many procedures for SAT-related problems, in particular for those requiring the complete enumeration of satisfying truth assignments, rely their efficiency and effectiveness on the detection of (possibly small) partial assignments…

A knowledge base is redundant if it contains parts that can be inferred from the rest of it. We study the problem of checking whether a CNF formula (a set of clauses) is redundant, that is, it contains clauses that can be derived from the…

Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. Non-rigorous statistical mechanics ideas have inspired a message passing algorithm called Belief Propagation Guided Decimation for finding satisfying…

This paper addresses the resolution of the 3-SAT problem using a QAOA-like approach. The chosen principle involves modeling the solution ranks of the 3-SAT problem, which, in this particular case, directly represent a solution. This results…

This paper introduces SATformer, a novel Transformer-based approach for the Boolean Satisfiability (SAT) problem. Rather than solving the problem directly, SATformer approaches the problem from the opposite direction by focusing on…

Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…

Let $\phi$ be a 3CNF formula with n variables and m clauses. A simple nonconstructive argument shows that when m is sufficiently large compared to n, most 3CNF formulas are not satisfiable. It is an open question whether there is an…

Whether the satisfiability of any formula F of propositional calculus can be determined in polynomial time is an open question. I propose a simple procedure based on some real world mechanisms to tackle this problem. The main result is the…

We present graph backtracking, a novel, fine-grained backtracking scheme for CDCL-based SAT solving, parametrized by a user-defined weight function. For conflict repair, we challenge the decision level abstraction and use the implication…

Gaussian conditional random fields (GCRF) are a well-known used structured model for continuous outputs that uses multiple unstructured predictors to form its features and at the same time exploits dependence structure among outputs, which…

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…

This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…

Some aspects of the result of applying unit resolution on a CNF formula can be formalized as functions with domain a set of partial truth assignments. We are interested in two ways for computing such functions, depending on whether the…

Graph Neural Networks (GNNs) have been a powerful tool for node classification tasks in complex networks. However, their decision-making processes remain a black-box to users, making it challenging to understand the reasoning behind their…