Final Activity Report Summary - ASFIX (Abstract Semantic Frameworks for Implicit Complexity) The research area this project can be ascribed to is theoretical computer science. In particular, it concerned implicit computational complexity and semantics, as described in the project proposal. The objective of the project was the design of a unifying abstract semantic framework for implicit computational complexity. Particular attention was given to semantic frameworks in the spirit of game semantics and geometry of interaction, since they were inherently capable of revealing the intensional properties of programs and proofs. During his stay in Paris, the fellow interacted with researchers working in the host institution, namely Olivier Laurent, Paul-André Mellies and Pierre-Louis Curien. This interaction led to the definition of a game-theoretical framework for multiplicative and exponential linear logic. In this framework, the complexity of normalisation of any proof could be read out of its interpretation. Noticeably, the process of measuring the complexity of any proof could be internalised in the semantics and the underlying logical system. The framework was designed based on the fellows previous work on context semantics, linear logic and computational complexity. On the other hand, the great skills and expertise of the host institution researchers in game semantics were absolutely vital during all project phases. A technical report was jointly written by the fellow and Olivier Laurent and an extended abstract was submitted to an international conference on logic in computer science.