Real quantifier elimination by cylindrical algebraic decomposition, and improvements by machine learning

Abstract

Given a quantified logical formula whose atoms are polynomial constraints with real valued variables, Real Quantifier Elimination (QE) means to derive a logically equivalent formula which does not involve quantifiers or the quantified variables from the original statement. For example, Real QE would reduce the statement that there exists a real solution x to the quadratic equation x2 + bx + c = 0 to the equivalent condition on the discriminant: b2 - 4c ≥ 0. Tarski proved Real QE is always possible (with sufficient resources) [7].