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 …

Real analysis is pervasive to many applications, if only because it is a suitable tool for
modeling physical or socio-economical systems. As such, its support is warranted in proof …

Roundoff errors cannot be avoided when implementing numerical programs with finite
precision. The ability to reason about rounding is especially important if one wants to …

Memory system reliability is a serious and growing concern in modern servers. Existing
chipkill-level memory protection mechanisms suffer from several drawbacks. They activate a …

This paper introduces a static analysis technique for computing formally verified round-off
error bounds of floating-point functional expressions. The technique is based on a …

In the recent years, numerous proof systems have improved enough to be used for formally
verifying non-trivial mathematical results. They, however, have different purposes and it is …

Differential dynamic logic (dL) is a formal framework for specifying and reasoning about
hybrid systems, ie, dynamical systems that exhibit both continuous and discrete behaviors …

This paper proposes a reliability analysis framework for systems subject to multiple design
requirements that depend polynomially on uncertain parameters. The values these …

The verification of floating-point mathematical libraries requires computing numerical
bounds on approximation errors. Due to the tightness of these bounds and the peculiar …