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Algorithms for active learning of small separating DFAs have many applications, e.g. for learning network invariants, learning contextual assumptions in compositional verification, learning state machines from large amounts of log data, and learning bug pattern descriptions. We propose a simple active learning algorithm, inspired by\n \n \n $$L^{\\#}$$<\/jats:tex-math>\n \n \n L<\/mml:mi>\n #<\/mml:mo>\n <\/mml:msup>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n , that learns a minimal separating DFA for disjoint languages\n \n \n $$L_1$$<\/jats:tex-math>\n \n \n L<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n and\n \n \n $$L_2$$<\/jats:tex-math>\n \n \n L<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n if one exists. Experiments show that our algorithm significantly outperforms existing active learning algorithms on both randomly generated and industrial benchmarks.\n <\/jats:p>","DOI":"10.1007\/978-3-032-32526-6_13","type":"book-chapter","created":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T08:47:14Z","timestamp":1784796434000},"page":"261-283","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An $$L^{\\#}$$ Based Algorithm for\u00a0Active Learning of\u00a0Minimal Separating Automata"],"prefix":"10.1007","author":[{"given":"Jasper","family":"Laumen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Leonne","family":"Snel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frits","family":"Vaandrager","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,7,24]]},"reference":[{"issue":"2","key":"13_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/0890-5401(87)90052-6","volume":"75","author":"D Angluin","year":"1987","unstructured":"Angluin, D.: Learning regular sets from queries and counterexamples. 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