Non-standard analysis and embedded software

One model for computing in the future is ubiquitous, embedded computational devices analogous to embedded electrical motors. Many of these computers will control physical objects and processes. Such hidden computerized environments introduce new safety and correctness concerns whose treatment go beyond present Formal Methods. In particular, one has to begin to speak about Real Space software in analogy with Real Time software. By this we mean, computerized systems which have to meet requirements expressed in the real geometry of space. How to translate such requirements into ordinary software specifications and how to carry out proofs is a major challenge. In this talk we propose a research program based on the use of no-standard analysis. Much detail remains to be carried out. The purpose of the talk is to inform the Formal Methods community that Non-Standard Analysis provides a possible avenue to attack which we believe will be fruitful.