Dr. Margarita Korovina
 Sobolev Inst of Math, Novosibirsk: 

"Sigma-definability and computability on continuous data types"


It is well-known that the classical theory of computation, which works
with discrete structures,is not suitable for formalisation of
computations that operate on real-valued data. Most computational
problems  in physics and engineering are of this type, e.g.  problems
relevant to foundation of dynamical and hybrid systems.
Since computational processes are discrete in their nature and
objects we consider are continuous,  formalisation of computability
of such objects is already a challenging research problem.
   In this talk we will report about logical approach to computability
on the reals based on  the notion of definability. In this approach
continuous objects and computational processes  involving these
objects can be defined using finite formulas.
        We will discuss beneficial features of this approach,
recent results and future work.