Uppsala University
Department of Information Technology

### Licentiate thesis 2006-003

# Regular Inference for Reactive Systems

### Therese Berg

27 April 2006

**Abstract:**
Models of reactive systems play a central role in many techniques for verification and analysis of reactive systems. Both a specification of the system and the abstract behavior of the system can be expressed in a formal model. Compliance with the functional parts in the specification can be controlled in different ways. Model checking techniques can be applied to a model of the system or directly to source code. In testing, model-based techniques can generate test suites from specification. A bottleneck in model-based techniques is however to construct a model of the system. This work concerns a technique that automatically constructs a model of a system without access to specification, code or internal structure. We assume that responses of the system to sequences of input can be observed. In this setting, so called regular inference techniques build a model of the system based on system responses to selected input sequences.

There are three main contributions in this thesis. The first is a survey on the most well-known techniques for regular inference. The second is an analysis of Angluin's algorithm for regular inference on synthesized examples. On a particular type of examples, with prefix-closed languages, typically used to model reactive systems, the required number of input sequences grow approximately quadratically in the number of transitions of the system. However, using an optimization for systems with prefix-closed languages we were able to reduce the number of required input sequences with about 20%. The third contribution is a developed regular inference technique for systems with parameters. This technique aims to better handle entities of communications protocols where messages normally have many parameters of which few determine the subsequent behavior of the system. Experiments with our implementation of the technique confirm a reduction of the required number of input sequences, in comparison with Angluin's algorithm.

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