The ReACT project was quite successful in establishing Complexity-through-Realisability techniques as a solid and promising new approach to computational complexity.
Concerning the first objective of the project, the expected characterisations of standard complexity classes were obtained, and it was shown how the method improves on standard techniques from Implicit Computational Complexity. Moreover, it was shown how the method applies to non-sequential models of computation, providing in particular sound mathematical models of probabilistic computation and of parallel random access machines.
Concerning the second objective a number of connections were discovered between standard tools and invariants of dynamical systems and the theory of Interaction Graphs, which underlies the Complexity-through-Realisability techniques. Building on this, it was possible to obtain a characterisation of a sufficient condition for two complexity classes to be equal. Some progress was also made concerning the question of showing that two classes are not equal, a major open problem in mathematics and computer science. Indeed we showed, using Complexity-through-Realisability methods, how several standard lower bounds results in complexity can be understood in terms of topological entropy, an invariant for dynamical systems.
Lastly, a number of additional results were obtained within the ReACT project through the collaboration with the supervisor and other researchers at the hosting institution. In particular it was shown that techniques related to Interaction Graphs could lead to methods in static analysis and optimisation of programs, which could be implemented within the LLVM compiler. Some theoretical results within the theory of dynamical systems were also obtained.
Overall, the project has lead to five publications in peer-reviewed venues (published or accepted), most of them in top-ranked venues, two tools/software, and seven papers currently submitted or in preparation.
