Verification of hybrid and continuous systems: results and problems
<P>                  Eugene Asarin (VERIMAG)


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Verification of hybrid and continuous system attracts resarchers'
effort during last 10-15 years. Around 1995 this domain seemed to
be well-explored: all interesting questions (except several
particular cases) proved to be undecidable.
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After a brief survey of these results I will discuss recent
progress in the domain. I will describe some "postmodern"
developments witnessing of richness and complexity of the area,
including the following questions: - beyond Church's thesis; -
noise and decidability, - between decidable and undecidable; -
acceleration for continuous systems.
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I will conclude by a comparison between the verification-based
approach to computability in the continuous domain and those of
computable analysis and algebraic complexity