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Simone Martini
** - Complexity of optimal sharing in Elementary linear logic

We will first quickly review the known results on optimal reduction in the lambda-calculus and its relations to linear logic. After discussing Asperti and Mairson's result that optimal lambda-reduction is not Kalmar elementary, we will show that optimal lambda-reduction remains non Kalmar elementary even for lambda-terms typeable in Girard's Elementary Linear Logic.