# An Abstract Framework for Counterexample Analysis in Active Automata Learning

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Malte Isberner,
Bernhard Steffen
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The 12th International Conference on Grammatical Inference, PMLR 34:79-93, 2014.

#### Abstract

Counterexample analysis has emerged as one of the key challenges in Angluin-style active automata learning. Rivest and Schapire (1993) showed for the \mathrmL^* algorithm that a single suffix of the counterexample was sufficient to ensure progress. This suffix can be obtained in a binary search fashion, requiring Θ(\log m) membership queries for a counterexample of length m. Correctly implementing this algorithm can be quite tricky, and its correctness sometimes even has been disputed. In this paper, we establish an abstract framework for counterexample analysis, which basically reduces the problem of finding a suffix to finding distinct neighboring elements in a 0/1 sequence, where the first element is 0 and the last element is 1. We demonstrate the conciseness and simplicity of our framework by using it to present new counterexample analysis algorithms, which, while maintaining the worst-case complexity of O(\log m), perform significantly better in practice. Furthermore, we contribute—in a second instantiation of our framework, highlighting its generality—the first sublinear counterexample analysis procedures for the algorithm due to Kearns and Vazirani (1994).

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