Section: New Results

Implicit Computational Complexity

Participants : Emmanuel Hainry, Romain Péchoux.

We have written a full journal paper, accepted in Information and Computation (special issue of DICE 2015), on the complexity analysis of Object Oriented programming languages based on tiered types. The corresponding type system provides sound and complete characterization of the set of polynomial time computable functions. As a consequence, the heap-space and the stack-space requirements of typed programs are also bounded polynomially. This type system is inspired by previous works on Implicit Computational Complexity, using tiering and non-interference techniques. The presented methodology has several advantages. First, it provides explicit big O polynomial upper bounds to the programmer, hence its use could allow the programmer to avoid memory errors. Second, type checking is decidable in polynomial time. Last, it has a good expressivity since it analyzes most object oriented features like inheritance, overload, override and recursion. Moreover it can deal with loops guarded by objects and can also be extended to statements that alter the control flow like break or return.