Among the various techniques for mining models from software systems, regular inference of black-box systems has been a central technique in the last decade. In this paper, we present various directions we have investigated for improving the efficiency of algorithms based on L~* in a software testing context where interactions with systems entail large and complex input domains. In particular we consider algorithmic optimizations for large input sets, for parameterized inputs, for processing counterexamples. We also present our current directions motivated by application to security testing: focusing on specific sequences, identifying randomly generated values, combining with other adaptive techniques.
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