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Instead of focusing on equivalence of observations, like the <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{*}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mrow>\n                      <mml:mrow\/>\n                      <mml:mo>\u2217<\/mml:mo>\n                    <\/mml:mrow>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> algorithm and its descendants, <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\#}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mo>#<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> takes a different perspective: it tries to establish <jats:italic>apartness<\/jats:italic>, a constructive form of inequality. <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\#}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mo>#<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> does not require auxiliary notions such as observation tables or discrimination trees, but operates directly on tree-shaped automata. <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\#}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mo>#<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> has the same asymptotic query and symbol complexities as the best existing learning algorithms, but we show that adaptive distinguishing sequences can be naturally integrated to boost the performance of <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\#}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mo>#<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> in practice. Experiments with a prototype implementation, written in Rust, suggest that <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^{\\#}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msup>\n                    <mml:mi>L<\/mml:mi>\n                    <mml:mo>#<\/mml:mo>\n                  <\/mml:msup>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is competitive with existing algorithms.<\/jats:p>","DOI":"10.1007\/978-3-030-99524-9_12","type":"book-chapter","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T06:14:55Z","timestamp":1648534495000},"page":"223-243","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["A New Approach for Active Automata Learning Based on Apartness"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3955-1910","authenticated-orcid":false,"given":"Frits","family":"Vaandrager","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4908-2863","authenticated-orcid":false,"given":"Bharat","family":"Garhewal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jurriaan","family":"Rot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8993-6486","authenticated-orcid":false,"given":"Thorsten","family":"Wi\u00dfmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,3,30]]},"reference":[{"key":"12_CR1","doi-asserted-by":"publisher","unstructured":"Aarts, F., Heidarian, F., Kuppens, H., Olsen, P., Vaandrager, F.: Automata learning through counterexample-guided abstraction refinement. 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