Robustness Analysis of Networked Systems

Many software systems are naturally modeled as networks of interacting elements such as computing nodes, input devices, and output devices. In this paper, we present a notion of robustness for a networked system when the underlying network is prone to errors. We model such a system

$\mathcal{N}$

as a set of processes that communicate with each other over a set of internal channels, and interact with the outside world through a fixed set of input and output channels. We focus on network errors that arise from channel perturbations, and assume that we are given a worst-case bound

δ

on the number of errors that can occur in the internal channels of

$\mathcal{N}$

. We say that the system

$\mathcal{N}$

is (

δ

,

ε

)-robust if the deviation of the output of the perturbed system from the output of the unperturbed system is bounded by

ε

.

We study a specific instance of this problem when each process is a Mealy machine, and the distance metric used to quantify the deviation from the desired output is either the

L

1

-norm or the Levenshtein distance (also known as the edit distance). For the former, we present a decision procedure for (

δ

,

ε

)-robustness that is polynomial in the size of the network. For the latter, we present a decision procedure that is polynomial in the size of the network and exponential in the error bound on the output channel. Our solution draws upon techniques from automata theory, essentially reducing the problem of checking (

δ

,

ε

)-robustness to the problem of checking emptiness for a certain class of reversal-bounded counter automata.