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This paper presents a new technique for optimizing formal analysis ofpropositional logic formulas and Linear Temporal Logic (LTL) formulas, namelythe formula simplification table. A formula simplification table is amathematical table that shows all possible simplifications of the formula underdifferent truth assignments of its variables. The advantages of constructing asimplification table of a formula are two-fold. First, it can be used tocompute the logical influence weight of each variable in the formula, which isa metric that shows the importance of the variable in affecting the outcome ofthe formula. Second, it can be used to identify variables that have the highestlogical influences on the outcome of the formula. %The simplification table canbe used to optimize %existing solutions for several interesting %LTLverification problems. We demonstrate the effectiveness of formulasimplification table in the context of software verification by developingefficient framework to the well-known decentralized LTL monitoring problem.

Efficient LTL Decentralized Monitoring Framework Using Formula Simplification Table