A message-passing interpretation of adjoint logic

Message Passing Logic

Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we introduce the categorical notion of a linear actegory and the related polycategorical notion of a poly-actegory. Not surprisingly the notation used for the te...

The logic of message passing

Message passing is a key ingredient of concurrent programming. The purpose of this paper is to describe the equivalence between the proof theory, the categorical semantics, and term calculus of message passing. In order to achieve this we introduce the categorical notion of a linear actegory and the related polycategorical notion of a poly-actegory. Not surprisingly the notation used for the te...

A Framework for Proving Correctness of Adjoint Message-Passing Programs

Adjoint programs play a central role in modern numerical algorithms such as large-scale sensitivity analysis, parameter tuning, and general nonlinear optimization. They can be generated automatically by compilers. In such cases, the data flow of the original program needs to be reversed. If message passing is used, then any communication needs to be reversed, too. Crucial properties of the orig...

An Operator Interpretation of Message Passing

Message passing algorithms may be viewed from a purely probabilistic or statistical physics perspective. This works describes an alternative, linear algebraic view of message passing in trees. We demonstrate the construction of global belief operators on Markov Chains and Trees and compare these with classical results. By interpreting message passing as finding a global stable solution we wish ...

Separation Logic - Expressiveness and Copyless Message-Passing