black-box/white-box simplification and applications to quantifier elimination
This paper describes a new method for simplifying Tarski formulas. The method combines simplifications based purely on the factor structure of inequalities ("black-box" simplification) with simplifications that require reasoning about the factors themselves. The goal is to produce a simplification procedure that is very fast, so that it can be applied --- perhaps many, many times --- within other algorithms that compute with Tarski formulas without ever slowing them down significantly, but which also produces useful simplification in a substantial number of cases. The method has been implemented and integrated into implementations of two important algorithms: quantifier elimination by virtual term substitution, and quantifier elimination by cylindrical algebraic decomposition. The paper reports on how the simplification method has been integrated with these two algorithms, and reports experimental results that demonstrate how their performance is improved.
simplification quantifier elimination tarski formulas