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Given an <jats:inline-formula><jats:tex-math>$$\\omega $$<\/jats:tex-math><\/jats:inline-formula>-regular winning condition <jats:inline-formula><jats:tex-math>$$\\varPhi $$<\/jats:tex-math><\/jats:inline-formula> for the system player, we compute an <jats:inline-formula><jats:tex-math>$$\\omega $$<\/jats:tex-math><\/jats:inline-formula>-regular assumption <jats:inline-formula><jats:tex-math>$$\\varPsi $$<\/jats:tex-math><\/jats:inline-formula> for the environment player, such that (i) every environment strategy compliant with <jats:inline-formula><jats:tex-math>$$\\varPsi $$<\/jats:tex-math><\/jats:inline-formula> allows the system to fulfill <jats:inline-formula><jats:tex-math>$$\\varPhi $$<\/jats:tex-math><\/jats:inline-formula> (sufficiency), (ii) <jats:inline-formula><jats:tex-math>$$\\varPsi $$<\/jats:tex-math><\/jats:inline-formula> can be fulfilled by the environment for every strategy of the system (implementability), and (iii) <jats:inline-formula><jats:tex-math>$$\\varPsi $$<\/jats:tex-math><\/jats:inline-formula> does not prevent any cooperative strategy choice (permissiveness).<\/jats:p><jats:p>For parity games, which are canonical representations of <jats:inline-formula><jats:tex-math>$$\\omega $$<\/jats:tex-math><\/jats:inline-formula>-regular games, we present a polynomial-time algorithm for the symbolic computation of <jats:italic>adequately permissive assumptions<\/jats:italic> and show that our algorithm runs faster and produces better assumptions than existing approaches\u2014both theoretically and empirically. To the best of our knowledge, for <jats:inline-formula><jats:tex-math>$$\\omega $$<\/jats:tex-math><\/jats:inline-formula><jats:italic>-regular<\/jats:italic> games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also <jats:italic>permissive<\/jats:italic>.<\/jats:p>","DOI":"10.1007\/978-3-031-30820-8_15","type":"book-chapter","created":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T19:02:36Z","timestamp":1681930956000},"page":"211-228","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Computing Adequately Permissive Assumptions for Synthesis"],"prefix":"10.1007","author":[{"given":"Ashwani","family":"Anand","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaushik","family":"Mallik","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Satya Prakash","family":"Nayak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anne-Kathrin","family":"Schmuck","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2023,4,20]]},"reference":[{"key":"15_CR1","unstructured":"The reactive synthesis competition. http:\/\/www.syntcomp.org"},{"key":"15_CR2","doi-asserted-by":"crossref","unstructured":"Anand, A., Mallik, K., Nayak, S.P., Schmuck, A.K.: Computing adequately permissive assumptions for synthesis (2023), https:\/\/arxiv.org\/abs\/2301.07563","DOI":"10.1007\/978-3-031-30820-8_15"},{"key":"15_CR3","unstructured":"Baier, C., Katoen, J.P.: Principles of model checking. 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