A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Thomas Sturm (1, 2, 3)

1 MPII - Max-Planck-Institut für Informatik
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
3 MOSEL - Proof-oriented development of computer-based systems

Effective quantifier elimination procedures for first-order theories provide a powerful tool for generically solving a wide range of problems based on logical specifications. In contrast to general first-order provers, quantifier elimination procedures are based on a fixed set of admissible logical symbolswith an implicitly fixed semantics. This admits the use of sub-algorithms from symbolic computation. We are going to focus on quantifier elimination for the reals and its applications giving examples from geometry, verification, and the life sciences. Beyond quantifier elimination we are going to discuss recent results with a subtropical procedure for an existential fragment of the reals. This incomplete decision procedure has been successfully applied to the analysis of reaction systems in chemistry and in the life sciences.

Mots clés: Real quantifier elimination and decision; Satisfiability; Virtual substit...; Subtropical methods; Real geometry; Verification; Reaction system...; Stability analysis

Domaines: Informatique [cs]

Thomas Sturm. A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications. Mathematics in Computer Science, 2017, 11 (3-4), pp.483 - 502. ⟨10.1007/s11786-017-0319-z⟩. ⟨hal-01648690⟩