Realizability models and implicit complexity

Realizability models and implicit complexity

New, simple, proofs of soundness (every representable function lies in a given complexity class) for Elementary Affine Logic, LFPL and Soft Affine Logic are presented. The proofs are obtained by instantiating a semantic framework previously introduced by the authors and based on an innovativemodification of realizability. The proof is a notable simplification on the original already semantic pr...

Realizability and implicit PTIME characterization

Quantitative Models and Implicit Complexity

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways...

Realizability of interaction models

In scenarios where a set of independent business partners engage in complex conversations, interaction models are a means to specify the allowed interaction behavior from a global perspective. Atomic interactions serve as basic building blocks and behavioral dependencies are defined between them. The notion of realizability centers around the question whether there exist a set of roles that col...

Towards a Complexity-through-Realizability Theory

We explain how recent developments in the fields of realizability models for linear logic [Sei14e] – or geometry of interaction – and implicit computational complexity [AS14, AS15] can lead to a new approach of implicit computational complexity. This semantic-based approach should apply uniformly to various computational paradigms, and enable the use of new mathematical methods and tools to att...