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While in general the problem is EXPTIMEcomplete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach. © 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.","lang":"eng"}],"external_id":{"arxiv":["1511.08456"]},"date_published":"2016-12-02T00:00:00Z","publication":"Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence","year":"2016","doi":"10.1609/aaai.v30i1.10422","acknowledgement":"The research was partly supported by Austrian Science Fund (FWF) Grant No P23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award.","date_created":"2018-12-11T11:50:30Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","conference":{"location":"Phoenix, AZ, United States","start_date":"2016-02-12","name":"AAAI: Conference on Artificial Intelligence","end_date":"2016-02-17"},"language":[{"iso":"eng"}],"project":[{"call_identifier":"FWF","_id":"2584A770-B435-11E9-9278-68D0E5697425","grant_number":"P 23499-N23","name":"Modern Graph Algorithmic Techniques in Formal Verification"},{"_id":"25832EC2-B435-11E9-9278-68D0E5697425","grant_number":"S 11407_N23","name":"Rigorous Systems Engineering","call_identifier":"FWF"},{"name":"Quantitative Graph Games: Theory and Applications","grant_number":"279307","_id":"2581B60A-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"type":"conference","title":"A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs","publication_status":"published","ec_funded":1,"article_processing_charge":"No","page":"3225 - 3232","citation":{"ieee":"K. Chatterjee, M. Chmelik, and J. Davies, “A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs,” in <i>Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence</i>, Phoenix, AZ, United States, 2016, vol. 2016, pp. 3225–3232.","chicago":"Chatterjee, Krishnendu, Martin Chmelik, and Jessica Davies. “A Symbolic SAT Based Algorithm for Almost Sure Reachability with Small Strategies in POMDPs.” In <i>Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence</i>, 2016:3225–32. AAAI Press, 2016. <a href=\"https://doi.org/10.1609/aaai.v30i1.10422\">https://doi.org/10.1609/aaai.v30i1.10422</a>.","ama":"Chatterjee K, Chmelik M, Davies J. A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs. In: <i>Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence</i>. Vol 2016. AAAI Press; 2016:3225-3232. doi:<a href=\"https://doi.org/10.1609/aaai.v30i1.10422\">10.1609/aaai.v30i1.10422</a>","short":"K. Chatterjee, M. Chmelik, J. Davies, in:, Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, AAAI Press, 2016, pp. 3225–3232.","ista":"Chatterjee K, Chmelik M, Davies J. 2016. A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs. Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence. AAAI: Conference on Artificial Intelligence vol. 2016, 3225–3232.","apa":"Chatterjee, K., Chmelik, M., &#38; Davies, J. (2016). A symbolic SAT based algorithm for almost sure reachability with small strategies in POMDPs. In <i>Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence</i> (Vol. 2016, pp. 3225–3232). Phoenix, AZ, United States: AAAI Press. <a href=\"https://doi.org/10.1609/aaai.v30i1.10422\">https://doi.org/10.1609/aaai.v30i1.10422</a>","mla":"Chatterjee, Krishnendu, et al. “A Symbolic SAT Based Algorithm for Almost Sure Reachability with Small Strategies in POMDPs.” <i>Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence</i>, vol. 2016, AAAI Press, 2016, pp. 3225–32, doi:<a href=\"https://doi.org/10.1609/aaai.v30i1.10422\">10.1609/aaai.v30i1.10422</a>."},"quality_controlled":"1","OA_type":"green","volume":2016,"publisher":"AAAI Press","intvolume":"      2016","OA_place":"repository","month":"12","date_updated":"2025-06-25T11:52:14Z","related_material":{"record":[{"relation":"earlier_version","status":"public","id":"5443"}],"link":[{"url":"https://dl.acm.org/citation.cfm?id=3016355","relation":"table_of_contents"}]},"oa":1,"publist_id":"6191","department":[{"_id":"KrCh"},{"_id":"ToHe"}],"arxiv":1,"corr_author":"1","_id":"1166","status":"public"},{"has_accepted_license":"1","citation":{"ieee":"K. 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We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. 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