Related papers: An Efficient Algorithm for Solving the 2-MAXSAT Pr…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
In this paper we propose a structural parameter of CNF formulas and use it to identify instances of weighted MaxSAT and #SAT that can be solved in polynomial time. Given a CNF formula we say that a set of clauses is precisely satisfiable if…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula $\varphi$ in CNF such that exactly one literal in each clause is assigned to be "1" and the other literals in the same clause…
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…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
In this paper, we examine Yangjun Chen's technical report titled ``The 2-MAXSAT Problem Can Be Solved in Polynomial Time'' [Che23], which revises and expands upon their conference paper of the same name [Che22]. Chen's paper purports to…
The Exact Satisfiability problem, XSAT, is defined as the problem of finding a satisfying assignment to a formula in CNF such that there is exactly one literal in each clause assigned to be 1 and the other literals in the same clause are…
Let F be a CNF formula with n variables and m clauses. F is 3-satisfiable if for any 3 clauses in F, there is a truth assignment which satisfies all of them. Lieberherr and Specker (1982) and, later, Yannakakis (1994) proved that in each…
In this paper we introduce "hybrid" Max 2-CSP formulas consisting of "simple clauses", namely conjunctions and disjunctions of pairs of variables, and general 2-variable clauses, which can be any integer-valued functions of pairs of boolean…
Majority-SAT is the problem of determining whether an input $n$-variable formula in conjunctive normal form (CNF) has at least $2^{n-1}$ satisfying assignments. Majority-SAT and related problems have been studied extensively in various AI…
An O(n+m)-time algorithm is presented for counting the number of models of a two Conjunctive Normal Form Formula F that represents a Cactus graph, where n is the number of variables and m is the number of clauses of F. Although, it was…
In MaxSat, we are given a CNF formula $F$ with $n$ variables and $m$ clauses and asked to find a truth assignment satisfying the maximum number of clauses. Let $r_1,..., r_m$ be the number of literals in the clauses of $F$. Then…
A pair of unit clauses is called conflicting if it is of the form $(x)$, $(\bar{x})$. A CNF formula is unit-conflict free (UCF) if it contains no pair of conflicting unit clauses. Lieberherr and Specker (J. ACM 28, 1981) showed that for…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
We consider constraint satisfaction problems parameterized above or below tight bounds. One example is MaxSat parameterized above $m/2$: given a CNF formula $F$ with $m$ clauses, decide whether there is a truth assignment that satisfies at…
In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
Given a 2-SAT formula $F$ consisting of $n$ variables and $\cn$ random clauses, what is the largest number of clauses $\max F$ satisfiable by a single assignment of the variables? We bound the answer away from the trivial bounds of…
In {\sc MaxSat}, we ask for an assignment which satisfies the maximum number of clauses for a boolean formula in CNF. We present an algorithm yielding a run time upper bound of $O^*(2^{\frac{1}{6.2158}})$ for {\sc Max-2-Sat} (each clause…
Graph neural networks (GNNs) have shown promising performance in solving both Boolean satisfiability (SAT) and Maximum Satisfiability (MaxSAT) problems due to their ability to efficiently model and capture the structural dependencies…