Shirac: A linear algebra for event-based system modeling

TL;DR

This paper introduces Shirac, a linear algebra framework inspired by event-based system modeling, connecting digital signal theory with computational models like graphs and networks for performance analysis.

Contribution

It extends Dirac comb concepts from signal theory to analyze computer performance, bridging electrical engineering methods with computation models.

Findings

Provides a new algebraic approach for event-based system analysis

Connects digital signal concepts to models of computation

Enables performance evaluation using linear algebra techniques

Abstract

Digital signal theory is an extension of the analysis of continuous signals. This extension is provided by discretization and sampling. The sampling of signals can be mathematically described by a series of Dirac impulses and is well known. Properties of the Dirac impulse, such as sampling, are derived in distribution theory. The theory generalizes differential calculus to functions that are not differentiable in the classical sense such as the Heaviside step function. Therefore, distribution theory allows one to adopt analog analysis concepts to digital signals. In this report, we extend the concept of Dirac combs, a series of Dirac impulses as known from signal theory, to performance analysis of computers. The goal is to connect methods from electrical engineering or physics to different models of computation such as graphs, and network as well as real-time calculus.