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A type system is introduced for a generic Object Oriented programminglanguage in order to infer resource upper bounds. A sound andcompletecharacterization of the set of polynomial time computable functions isobtained. As a consequence, the heap-space and thestack-space requirements oftyped programs are also bounded polynomially. This type system is inspired byprevious works on ImplicitComputational Complexity, using tiering andnon-interference techniques. The presented methodology has several advantages.First, itprovides explicit big $O$ polynomial upper bounds to the programmer,hence its use could allow the programmer to avoid memory errors.Second, typechecking is decidable in polynomial time. Last, it has a good expressivitysince it analyzes most object oriented featureslike inheritance, overload,override and recursion. Moreover it can deal with loops guarded by objects andcan also be extended tostatements that alter the control flow like break orreturn.

A Type-Based Complexity Analysis of Object Oriented Programs