# State Identification for Labeled Transition Systems with Inputs and Outputs

## TL;DR

This paper introduces an algorithm for state identification in labeled transition systems with inputs and outputs, extending FSM testing theory to more complex systems and demonstrating high effectiveness in practical benchmarks.

## Contribution

It generalizes the adaptive distinguishing sequence algorithm from FSMs to LTSs, enabling effective state identification in richer system models.

## Key findings

- Algorithm distinguishes over 99% of incompatible state pairs in benchmarks.
- The approach extends FSM testing techniques to LTSs, broadening applicability.
- Experimental results show practical effectiveness despite theoretical limitations.

## Abstract

For Finite State Machines (FSMs) a rich testing theory has been developed to discover aspects of their behavior and ensure their correct functioning. Although this theory is widely used, e.g., to check conformance of protocol implementations, its applicability is limited by restrictions of the FSM framework: the fact that inputs and outputs alternate in an FSM, and outputs are fully determined by the previous input and state. Labeled Transition Systems with inputs and outputs (LTSs), as studied in ioco testing theory, provide a richer framework for testing component oriented systems, but lack the algorithms for test generation from FSM theory. In this article, we propose an algorithm for the fundamental problem of state identification during testing of LTSs. Our algorithm is a direct generalization of the well-known algorithm for computing adaptive distinguishing sequences for FSMs proposed by Lee & Yannakakis. Our algorithm has to deal with so-called compatible states, states that cannot be distinguished in case of an adversarial system-under-test. Analogous to the result of Lee & Yannakakis, we prove that if an (adaptive) test exists that distinguishes all pairs of incompatible states of an LTS, our algorithm will find one. In practice, such adaptive tests typically do not exist. However, in experiments with an implementation of our algorithm on an industrial benchmark, we find that tests produced by our algorithm still distinguish more than 99% of the incompatible state pairs.