Message passing over factor graph can be considered as generalization of many well known algorithms for efficient marginalization of multivariate function. A specific instance of the algorithm is obtained by choosing an appropriate commutative semiring for the range of the function to be marginalized. Some examples are Viterbi algorithm, obtained on max-product semiring and forward-backward alg...

In this chapter we examine two fundamental, although low-level, approaches to expressing parallelism in programs. Over the years, numerous different approaches to designing and implementing parallel programs have been developed (e.g., see the excellent survey article by Skillicorn and Talia [870]). However, over time, two dominant alternatives have emerged: message passing and multithreading. T...

This paper studies the characteristics of synchronous ordering of messages. Synchronous ordering of messages deenes synchronous communication based on the causality relation rather than time. We present the necessary characteristics of any algorithm providing deadlock-free synchronous ordering of the messages. We also present the suucient conditions, based on the causality relations, for any al...

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...

In this report we document a software package under development to allow message passing in the MPI model using the computer algebra system Maple. The new software, called maplle, consists of two components, a set of Maple functions and a MPI/C driver. The maplle system allows the user to easily parallelize Maple algorithms and use message passing functionality familiar to MPI users in a Maple ...