Currently best known upper bounds for many NP-hard problems are obtained by using divide-and-conquer (splitting) algorithms. Roughly speaking, there are two ways of splitting algorithm improvement: a more involved case analysis and an introduction of a new simplification rule. It is clear that case analysis can be executed by computer, so it was considered as a machine task. Recently, several programs for automated case analysis were implemented. However, designing a new simplification rule is usually considered as a human task. In this paper we show that designing simplification rules can also be automated. We present several new (previously unknown) automatically generated simplification rules for the SAT and MAXSAT problems. The new approach allows not only to generate simplification rules, but also to find good splittings. To illustrate our technique we present a new algorithm for (n, 3)-MAXSAT that uses both splittings and simplification rules based on our approach and has worst-case running time O(1.2721~NL), where N is the number of variables and L is the length of an input formula. This bound improves the previously known bound O(1.3248~NL) of Bansal and Raman.
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