Section: New Results

Implicit Computational Complexity

In the setting of non-interference and implicit computational complexity, Emmanuel Hainry, Jean-Yves Marion, and Romain Péchoux presented a characterization of FPSPACE in a language with a fork/wait mechanism [20] . The language used in this work is a classical imperative language with while loops complemented with a mechanism to launch new processes through forks. The fork instruction is heavily inspired by C's fork/wait construction for Unix operating systems, which anchors this work in a down-to-earth setting. Using a type system that enforces a data-ramification on variables, they show that all programs that can be typed and are terminating compute an FPSPACE function, that with a natural evaluation strategy, they indeed use only polynomial space, and conversely that this type system is complete as all FPSPACE functions can be implemented in this language in a typable way.

Emmanuel Hainry and Romain Péchoux also used data-ramification combined with non-interference principles to effectively bound the memory used by object oriented languages in [21] . This work introduces a type system for an object oriented language (derived from java). This type system allows to compute polynomial bounds on the heap and stack used by a typable program, ensuring that if the program halts, it will only use memory under this explicit bound. As the typing procedure is doable in time polynomial in the size of the program, those bounds are easy to obtain, though not tight. Interesting features of this work include inheritance (with overloading and overriding) and, the ability to analyze programs with flow statements controled by objects, contrary to most other works in implicit computational complexity. In [24] , Romain Péchoux has shown that the notion of (polynomial) interpretation over term rewrite systems can be adapated on a process language, a variant of the pi-calculus with process recursive definitions. This work shows that the order induced by simulation can be used wrt a given process semantics to infer time and space upper bounds on process resource usage (reduction length, size of sent values, ...).