An Algebra of Synchronous Scheduling Interfaces

TL;DR

This paper introduces an algebraic framework for synchronous scheduling interfaces that combines logical and quantitative methods, enabling precise analysis of worst-case timing and scheduling in concurrent systems.

Contribution

It presents a novel algebraic approach based on modal logic and min-max arithmetic for specifying and analyzing synchronous interfaces and their scheduling bounds.

Findings

Provides a formal algebraic model for synchronous scheduling

Enables precise worst-case timing analysis in concurrent systems

Demonstrates applicability through network flow and task scheduling examples

Abstract

In this paper we propose an algebra of synchronous scheduling interfaces which combines the expressiveness of Boolean algebra for logical and functional behaviour with the min-max-plus arithmetic for quantifying the non-functional aspects of synchronous interfaces. The interface theory arises from a realisability interpretation of intuitionistic modal logic (also known as Curry-Howard-Isomorphism or propositions-as-types principle). The resulting algebra of interface types aims to provide a general setting for specifying type-directed and compositional analyses of worst-case scheduling bounds. It covers synchronous control flow under concurrent, multi-processing or multi-threading execution and permits precise statements about exactness and coverage of the analyses supporting a variety of abstractions. The paper illustrates the expressiveness of the algebra by way of some examples taken from network flow problems, shortest-path, task scheduling and worst-case reaction times in synchronous programming.