Cyber-physical systems combine cyber capabilities with physical capabilities to solve
problems that neither part could solve alone. This chapter provides an informal introduction …

We propose a new decision procedure for the existential theory of the reals. It performs a
backtracking search for a model in R, where the backtracking is powered by a novel conflict …

This paper presents a formalization in higher-order logic of a practical representation of
multivariate Bernstein polynomials. Using this representation, an algorithm for finding lower …

High-performance SMT solvers contain many tightly integrated, hand-crafted heuristic
combinations of algorithmic proof methods. While these heuristic combinations tend to be …

This paper presents raSAT SMT solver, which is aimed to handle polynomial constraints
over both reals and integers with simple unified methodologies. Its three main features are …

Quantifier-free nonlinear arithmetic (QF_NRA) appears in many applications of satisfiability
modulo theories solving (SMT). Accordingly, efficient reasoning for corresponding …

Many deep issues plaguing today's financial markets are symptoms of a fundamental
problem: The complexity of algorithms underlying modern finance has significantly outpaced …

This paper presents a formally verified quantifier elimination (QE) algorithm for first-order
real arithmetic by linear and quadratic virtual substitution (VS) in Isabelle/HOL. The Tarski …

Hybrid systems with both discrete and continuous dynamics are an important model for real-
world cyber-physical systems. The key challenge is to ensure their correct functioning wrt …

We address satisfiability checking for the first-order theory of the real-closed field (RCF)
using satisfiability-modulo-theories (SMT) solving. SMT solvers combine a SAT solver to …