We describe the open-source tool dReal, an SMT solver for nonlinear formulas over the
reals. The tool can handle various nonlinear real functions such as polynomials …

We introduce the notion of “δ-complete decision procedures” for solving SMT problems over
the real numbers, with the aim of handling a wide range of nonlinear functions including …

A number of powerful and scalable hybrid systems model checkers have recently emerged.
Although all of them honor roughly the same hybrid systems semantics, they have drastically …

We study SMT problems over the reals containing ordinary differential equations,. They are
important for formal verification of realistic hybrid systems and embedded software. We …

This article proves the completeness of an axiomatization for differential equation invariants
described by Noetherian functions. First, the differential equation axioms of differential …

The real numbers are pervasive, both in daily life, and in mathematics. Students spend much
time studying their properties. Yet computers and programming languages generally provide …

It has been challenging for the technical and regulatory communities to formulate
requirements for trustworthiness of the cyber-physical systems (CPS) due to the complexity …

We combine reachability analysis and probability bounds analysis, which allow for
imprecisely known random variables (multivariate intervals or p-boxes) to be specified as …

In this paper, we survey recent work on the use of statistical model checking techniques for
biological applications. We begin with an overview of the basic modelling techniques for …

We present the STLmc model checker for signal temporal logic (STL) properties of hybrid
systems. The STLmc tool can perform STL model checking up to a robustness threshold for …