What packets may come: automata for network monitoring

We consider the problem of monitoring an interactive device, such as an implementation of a network protocol, in order to check whether its execution is consistent with its specification. At rst glance, it appears that a monitor could simply follow the input-output trace of the device and check it against the specification. However, if the monitor is able to observe inputs and outputs only from a vantage point external to the device---as is typically the case---the problem becomes surprisingly difficult. This is because events may be bu ered, and even lost, between the monitor and the device, in which case, even for a correctly running device, the trace observed at the monitor could be inconsistent with the specification.In this paper, we formulate the problem of external monitoring as a language recognition problem. Given a specification that accepts a certain language of input-output sequences, we de ne another language that corresponds to input-output sequences observable externally. We also give an algorithm to check membership of a string in the derived language. It turns out that without any assumptions on the specification, this algorithm may take unbounded time and space. To address this problem, we de ne a series of properties of device specifications or protocols that can be exploited to construct e cient language recognizers at the monitor. We characterize these properties and provide complexity bounds for monitoring in each case.To illustrate our methodology, we describe properties of the Internet Transmission Control Protocol (TCP), and identify features of the protocol that make it challenging to monitor e ciently.