相关论文: Maximizing the Number of Satisfied L-clauses

Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of $k$-clauses is $p$-satisfiable if there exists a…

Given a CNF formula $\Phi$ with clauses $C_1,\ldots,C_m$ and variables $V=\{x_1,\ldots,x_n\}$, a truth assignment $a:V\rightarrow\{0,1\}$ of $\Phi$ leads to a clause sequence $\sigma_\Phi(a)=(C_1(a),\ldots,C_m(a))\in\{0,1\}^m$ where $C_i(a)…

We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…

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…

To test incomplete search algorithms for constraint satisfaction problems such as 3-SAT, we need a source of hard, but satisfiable, benchmark instances. A simple way to do this is to choose a random truth assignment A, and then choose…

The technical report presents a generic exact solution approach for minimizing the project duration of the resource-constrained project scheduling problem with generalized precedences (Rcpsp/max). The approach uses lazy clause generation,…

We call a CNF formula linear if any two clauses have at most one variable in common. Let Linear k-SAT be the problem of deciding whether a given linear k-CNF formula is satisfiable. Here, a k-CNF formula is a CNF formula in which every…

Boolean satisfiability problem has applications in various fields. An efficient algorithm to solve satisfiability problem can be used to solve many other problems efficiently. The input of satisfiability problem is a finite set of clauses.…

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…

We obtain the smallest unsatisfiable formulas in subclasses of $k$-CNF (exactly $k$ distinct literals per clause) with bounded variable or literal occurrences. Smaller unsatisfiable formulas of this type translate into stronger…

We focus on the random generation of SAT instances that have properties similar to real-world instances. It is known that many industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

(k,s)-SAT is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times. It is known that there exists a function f such that for s\leq f(k) all (k,s)-SAT instances…

The problem of identifying the satisfiability threshold of random $3$-SAT formulas has received a lot of attention during the last decades and has inspired the study of other threshold phenomena in random combinatorial structures. The…

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…

A generalized 1-in-3SAT problem is defined and found to be in complexity class P when restricted to a certain subset of CNF expressions. In particular, 1-in-kSAT with no restrictions on the number of literals per clause can be decided in…

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…

The Random Satisfiability problem has been intensively studied for decades. For a number of reasons the focus of this study has mostly been on the model, in which instances are sampled uniformly at random from a set of formulas satisfying…

This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…

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…