Since hybrid embedded systems are pervasive and often safety-critical, guarantees about their correct performance are desirable. The hybrid systems model checker HyTech provides such guarantees and has successfully veriied some systems. However, HyTech severely restricts the continuous dynamics of the system being analyzed and, therefore, often forces the use of prohibitively expensive discrete...

This paper presents a branch & cut algorithm to nd all isolated solutions of a system of polynomial constraints. Our ndings show that fairly straightforward reenements of interval methods inspired by AI constraint propagation techniques result in a multivariate root nding algorithm that is competitive with continuation methods on most benchmarks and which can solve a variety of systems that are...

This chapter contains selected papers presented at the Minisymposium on Interval Methods of the PARA’04 Workshop “State-ofthe-Art in Scientific Computing”. The emphasis of the workshop was on high-performance computing (HPC). The ongoing development of ever more advanced computers provides the potential for solving increasingly difficult computational problems. However, given the complexity of ...