{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/computing-adequately-permissive-assumptions","title":"Computing Adequately Permissive Assumptions for Synthesis","arxiv_id":"2301.07563","date":"2023-01-18","proceeding":null,"authors":["Ashwani Anand","Kaushik Mallik","Satya Prakash Nayak","Anne-Kathrin Schmuck"],"abstract":"We solve the problem of automatically computing a new class of environment assumptions in two-player turn-based finite graph games which characterize an ``adequate cooperation'' needed from the environment to allow the system player to win. Given an $\\omega$-regular winning condition $\\Phi$ for the system player, we compute an $\\omega$-regular assumption $\\Psi$ for the environment player, such that (i) every environment strategy compliant with $\\Psi$ allows the system to fulfill $\\Phi$ (sufficiency), (ii) $\\Psi$ can be fulfilled by the environment for every strategy of the system (implementability), and (iii) $\\Psi$ does not prevent any cooperative strategy choice (permissiveness). For parity games, which are canonical representations of $\\omega$-regular games, we present a polynomial-time algorithm for the symbolic computation of adequately permissive assumptions and show that our algorithm runs faster and produces better assumptions than existing approaches -- both theoretically and empirically. To the best of our knowledge, for $\\omega$-regular games, we provide the first algorithm to compute sufficient and implementable environment assumptions that are also permissive.","url_abs":"https://arxiv.org/abs/2301.07563v2","url_pdf":"https://arxiv.org/pdf/2301.07563v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"computing-adequately-permissive-assumptions","repo_url":"https://gitlab.mpi-sws.org/kmallik/simpa","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}