  This paper presents a new technique for optimizing formal analysis of
propositional logic formulas and Linear Temporal Logic (LTL) formulas, namely
the formula simplification table. A formula simplification table is a
mathematical table that shows all possible simplifications of the formula under
different truth assignments of its variables. The advantages of constructing a
simplification table of a formula are two-fold. First, it can be used to
compute the logical influence weight of each variable in the formula, which is
a metric that shows the importance of the variable in affecting the outcome of
the formula. Second, it can be used to identify variables that have the highest
logical influences on the outcome of the formula. %The simplification table can
be used to optimize %existing solutions for several interesting %LTL
verification problems. We demonstrate the effectiveness of formula
simplification table in the context of software verification by developing
efficient framework to the well-known decentralized LTL monitoring problem.
