{"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/shepherding-hordes-of-markov-chains","title":"Shepherding Hordes of Markov Chains","arxiv_id":"1902.05727","date":"2019-02-15","proceeding":null,"authors":["Milan Ceska","Nils Jansen","Sebastian Junges","Joost-Pieter Katoen"],"abstract":"This paper considers large families of Markov chains (MCs) that are defined\nover a set of parameters with finite discrete domains. Such families occur in\nsoftware product lines, planning under partial observability, and sketching of\nprobabilistic programs. Simple questions, like `does at least one family member\nsatisfy a property?', are NP-hard. We tackle two problems: distinguish family\nmembers that satisfy a given quantitative property from those that do not, and\ndetermine a family member that satisfies the property optimally, i.e., with the\nhighest probability or reward. We show that combining two well-known\ntechniques, MDP model checking and abstraction refinement, mitigates the\ncomputational complexity. Experiments on a broad set of benchmarks show that in\nmany situations, our approach is able to handle families of millions of MCs,\nproviding superior scalability compared to existing solutions.","url_abs":"http://arxiv.org/abs/1902.05727v2","url_pdf":"http://arxiv.org/pdf/1902.05727v2.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":"abstracts"},"code_links":[{"paper_slug":"shepherding-hordes-of-markov-chains","repo_url":"https://github.com/moves-rwth/shepherd","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}