A new approach on distributed systems: orderings and representability

TL;DR

This paper introduces a novel approach to distributed systems using total orders and biorders to model processes and communications, linking concepts from economics and computing, and develops methods for their numerical representability.

Contribution

It presents a new framework for modeling distributed systems with order structures and explores their representability, including a construction method for multi-utility representations.

Findings

Developed a model of distributed systems using total orders and biorders.

Established a construction method for finite Richter-Peleg multi-utility representations.

Linked order theory concepts to applications in economics and computer science.

Abstract

In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of `quasi-finite partial orders' is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter-Peleg multi-utility representation.