  Convex polyhedra are the basis for several abstractions used in static
analysis and computer-aided verification of complex and sometimes mission
critical systems. For such applications, the identification of an appropriate
complexity-precision trade-off is a particularly acute problem, so that the
availability of a wide spectrum of alternative solutions is mandatory. We
survey the range of applications of polyhedral computations in this area; give
an overview of the different classes of polyhedra that may be adopted; outline
the main polyhedral operations required by automatic analyzers and verifiers;
and look at some possible combinations of polyhedra with other numerical
abstractions that have the potential to improve the precision of the analysis.
Areas where further theoretical investigations can result in important
contributions are highlighted.
