Satisfiability Solving Research Papers - Academia.edu (original) (raw)

The boolean satisfiability problem was the first example of a NP-complete problem: a boolean formula can only be considered satisfiable if there is a set of variable bindings that evaluates said formula to true. The task of finding such solution is done by so-called SAT solvers. This project nevertheless focuses on constructing a solver for propositional formulae based on the DPLL algorithm, realizing the Watched Literals technique. Exploration will also be done regarding the performance impact of the implementation decisions, followed by further discussion about possible optimizations.

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- Algorithms for Satisfiability, Boolean Algebra, Satisfiability Solving, Dpll

Stochastic search methods tend to outperform systematic search approaches in solving randomly generated SAT problems. Typically, stochastic local search algorithms like WalkSAT can solve hard, randomly generated problems that are significantly larger than those handled by traditional complete search algorithms like DPLL or naive search techniques. However, unlike latters, local search algorithms are not complete and, as a consequence, cannot prove unsatisfiability. Therefore it is desirable to find a suitable probability and an enough large number of loops in WalkSAT for specific cases to prove satisfiability. Furthermore in the paper the advanced brute force search method is presented with the prune technique that proves that it is better than DPLL in runtime. Finally, the order of checking pure symbol and unit clause in DPLL is also considered to determine which has the runtime is better. Experiments are carried out on large data sets to evaluate the on both the runtime and the satisfiable percentages of these methods.

- by Giao Bui
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- Satisfiability Solving

We introduce the notion of reinforcement quantum annealing (RQA) scheme in which an intelligent agent searches in the space of Hamiltonians and interacts with a quantum annealer that plays the stochastic environment role of learning automata. At each iteration of RQA, after analyzing results (samples) from the previous iteration, the agent adjusts the penalty of unsatisfied constraints and re-casts the given problem to a new Ising Hamiltonian. As a proof-of-concept, we propose a novel approach for casting the problem of Boolean satisfiability (SAT) to Ising Hamiltonians and show how to apply the RQA for increasing the probability of finding the global optimum. Our experimental results on two different benchmark SAT problems (namely factoring pseudo-prime numbers and random SAT with phase transitions), using a D-Wave 2000Q quantum processor, demonstrated that RQA finds notably better solutions with fewer samples, compared to the best-known techniques in the realm of quantum annealing.

- by Tim Finin
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- Quantum Computing, Reinforcement Learning, Satisfiability Solving, quantum annealing

Home and Building Automation Systems (HBAS) are becoming of widespread adoption. When distinct users interact with such systems, their intentions are likely to be different, often resulting in conflicting situations, which the systems ought to recognize and resolve automatically. This work aims at investigating conflict in HBAS and creating a solution to detect and resolve them. Herein, we review the literature concerning conflict detection and resolution, and propose a formal framework based on constraint solving that enables detecting and solving conflict situations automatically.

In this paper I describe the progress, preliminary results and future work directions of a project of implementing a many-valued SAT solver based on a generalization of algorithms used in modern Boolean SAT solvers. Mimicking Boolean SAT solvers minimizes the algorithm-design and implementation challenges related to such a task, since many ideas can be easily adapted to the many-valued setting. Experimental results show that even on the early stages of the development a many-valued solver can perform better on some problems than modern Boolean SAT solvers.

- by Ines Lynce
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- Frequent Itemset Mining, Satisfiability Solving

The Boolean Satisfiability Problem (SAT) belongs to the class of NP-complete problems, meaning that there is no known deterministic algorithm that can solve an arbitrary problem instance in less than exponential time (parametrized on the length of the input). There is great industrial demand for solving SAT, motivating the need for algorithms which perform well. I present a comparison of two approaches for solving SAT instances: DPLL (an exact algorithm from classical computer science) and Survey Propagation (a probabilistic algorithm from statistical physics). The two algorithms were compared on randomly generated 3-SAT problems with varying clause to variable ratios.

- by Rui Henriques
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- Frequent Itemset Mining, Satisfiability Solving

Propositional satisfiability (SAT) problem is fundamental to the theory of NP-completeness. Indeed, using the concept of "polynomial-time reducibility" all NP-complete problems can be polynomially reduced to SAT. Thus, any new technique for satisfiability problems will lead to general approaches for thousands of hard combinatorial problems. In this paper, we introduce the incremental propositional satisfiability problem that consists of maintaining the satisfiability of a propositional formula anytime a conjunction of new clauses is added. More precisely, the goal here is to check whether a solution to a SAT problem continues to be a solution anytime a new set of clauses is added and if not, whether the solution can be modified efficiently to satisfy the old formula and the new clauses. We will study the applicability of systematic and approximation methods for solving incremental SAT problems. The systematic method is based on the branch and bound technique while the approximation methods rely on stochastic local search and genetic algorithms. Experimental tests, conducted on randomly generated SAT instances, demonstrate the efficiency in time of the approximation methods over the branch and bound algorithm. However these approximation methods do not always guarantee the completeness of the solution returned. We show that a method we propose that uses non systematic search in a limited form together with branch and bound has the best compromise, in practice, between time and quality of the solution returned (success ratio).

Multiway Decision Graph (MDG) is a canonical representation of a subset of many-sorted first-order logic. It generalizes the logic of equality with abstract types and uninterpreted function symbols. The area of Satisfiability (SAT) has been the subject of intensive research in recent years, with significant theoretical and practical contributions.