Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API

We consider the incremental computation of minimal unsatisfiable cores (MUCs) of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a novel API to allow for incremental solving based on clause groups. A clause group is a set of clauses which is incrementally added to or removed from a previously solved QBF. Our implementation of the novel API is related to incremental SAT solving based on selector variables and assumptions. However, the API entirely hides selector variables and assumptions from the user, which facilitates the integration of DepQBF in other tools. We present implementation details and, for the first time, report on experiments related to the computation of MUCs of QBFs using DepQBF's novel clause group API.Comment: (fixed typo), camera-ready version, 6-page tool paper, to appear in proceedings of SAT 2015, LNCS, Springe

Robust Artificial Immune System in the Hopfield network for Maximum k-Satisfiability

Artificial Immune System (AIS) algorithm is a novel and vibrant computational paradigm, enthused by the biological immune system. Over the last few years, the artificial immune system has been sprouting to solve numerous computational and combinatorial optimization problems. In this paper, we introduce the restricted MAX-kSAT as a constraint optimization problem that can be solved by a robust computational technique. Hence, we will implement the artificial immune system algorithm incorporated with the Hopfield neural network to solve the restricted MAX-kSAT problem. The proposed paradigm will be compared with the traditional method, Brute force search algorithm integrated with Hopfield neural network. The results demonstrate that the artificial immune system integrated with Hopfield network outperforms the conventional Hopfield network in solving restricted MAX-kSAT. All in all, the result has provided a concrete evidence of the effectiveness of our proposed paradigm to be applied in other constraint optimization problem. The work presented here has many profound implications for future studies to counter the variety of satisfiability problem

QBF with Soft Variables

QBF formulae are usually considered in prenex form, i.e. the quantifierblock is completely separated from the propositional part of the QBF.Among others, the semantics of the QBF is defined by the sequence ofthe variables within the prefix, where existentially quantifiedvariables depend on all universally quantified variables stated to theleft.In this paper we extend that classical definition and consider a newquantification type which we call soft variable. The idea is toallow a flexible position and quantifier type for these variables.Hence the type of quantifier of the soft variable can also bealtered. Based on this concept, we present an optimization problemseeking an optimal prefix as defined by user-given preferences. We statean algorithm based on MaxQBF, and present several applications – mainlyfrom verification area – which can be naturally translated into theoptimization problem for QBF with soft variables. We further implementeda prototype solver for this formalism, and compare our approach toprevious work, that differently from ours does not guarantee optimalityand completeness

Discrete hopfield neural network in restricted maximum k-satisfiability logic programming

Maximum k-Satisfiability (MAX-kSAT) consists of the most consistent interpretation that generate the maximum number of satisfied clauses. MAX-kSAT is an important logic representation in logic programming since not all combinatorial problem is satisfiable in nature. This paper presents Hopfield Neural Network based on MAX-kSAT logical rule. Learning of Hopfield Neural Network will be integrated with Wan Abdullah method and Sathasivam relaxation method to obtain the correct final state of the neurons. The computer simulation shows that MAX-kSAT can be embedded optimally in Hopfield Neural Network