A Deciding Algorithm for Linear Isomorphism of Types with Complexity O (n log2(n))

It is known, that ordinary isomorphisms (associativity and commutativity of \times", isomorphisms for \times" unit and currying) provide a complete axiomatisation of isomorphism of types in multiplica-tive linear lambda calculus (isomorphism of objects in a free symmetric monoidal closed category). One of the reasons to consider linear isomor-phism of types instead of ordinary isomorphism was that better complexity could be expected. Meanwhile, no upper bounds reasonnably close to linear were obtained. We describe an algorithm deciding if two types are linearly isomorphic with complexity O(nlog 2 (n)).