- Published 2005

Real-world systems can often be modelled by systems consisting of states and transitions between these states, triggered by certain events. These systems are called discrete event systems [4]. We are interested in the creation of such an event system for the detection of different types of behavior within a real-world system. The detection takes place using time series data from different kinds of sensors. Usually a set of pre-specified patterns is given, partially identifying the events which should be detected in the time series data. Given this set, it is often unknown or hard to specify which pattern exactly identifies an event. Therefore it is common to construct a classifier from labelled data-sets, which given new data determines what label is most likely to belong to the data. In our project we want to infer behavioral patterns (in particular driving behavior) using low-level sensor data. Given a partial description of a pattern and some labelled low-level data we want to infer an event system which identifies the pattern. A common model of an event system is a finite automaton (FA). An advantage of this model is the intuitive framework, i.e. the model can be interpreted by domain experts. A problem, however, is that FAs fail to model an important part of many real-world event systems, namely the timed relations between events. Real-world system behavior can often be described by a sequence of specific events, which are related to each other by the time at which they occur. For example, in our project the time between vehicle speedups and slowdowns is significant. A sequence of fast changes from slowing down to speeding up and vice versa indicates driving in a city, while a sequence of slow changes indicates driving on a freeway. The model of a FA which includes the notion of time is called a timed automaton (TA), first introduced by Alur and Dill (see [1]). In this model, each symbol of a word occurs at a certain point in time and the transitions between system states contain guards, i.e. constraints on these time points. The inference of FAs is a well-studied problem in learning theory. There are, however, almost no studies of the inference of TAs (or timed systems in general) from data. One approach to the inference of timed systems is a transformation method proposed by Grinchtein et al. [7]. They show that an event recording automaton (ERA) is learnable by transforming it into a deterministic finite automaton (DFA). The resulting DFA can be learned using a modified version of a learning algorithm. Unfortunately, however, in the

@inproceedings{Verwer2005TimedAF,
title={Timed Automata for Behavioral Pattern Recognition},
author={Sicco Verwer and Mathijs de Weerdt and Cees Witteveen},
year={2005}
}