Title: Community-based 3-SAT formulas with a predefined solution

Authors: Yamin Hu; Wenjian Luo; Junteng Wang

Addresses: School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China ' School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China; School of Computer Science and Technology, Harbin Institute of Technology, Harbin, Shenzhen, China ' School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China

Abstract: It is crucial to generate SAT formulas with predefined solutions for the development of SAT solvers since many SAT formulas from real-world applications have solutions. Although some algorithms have been proposed to generate SAT formulas with predefined solutions, community structures of SAT formulas are not considered in these algorithms. Consequently, we propose a 3-SAT formula generating algorithm that not only guarantees the existence of a predefined solution, but also simultaneously considers community structures and clause distributions. To study the effect of community structures and clause distributions on the hardness of SAT formulas, we measure solving runtimes of two solvers, gluHack and CPSparrow, on the generated SAT formulas under different parameter settings. Through extensive experiments, we obtain some noteworthy observations. For example, the community structure has few or no effects on the hardness of SAT formulas with regard to CPSparrow but a strong effect with regard to gluHack.

Keywords: SAT generator; community structure; predefined solution.

DOI: 10.1504/IJWMC.2021.121603

International Journal of Wireless and Mobile Computing, 2021 Vol.21 No.4, pp.310 - 322

Received: 20 Aug 2020
Accepted: 05 Jan 2021
Published online: 21 Mar 2022 *

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