{"id":"https://openalex.org/W2135245897","doi":"https://doi.org/10.1145/1755952.1755988","title":"On the connections between PCTL and dynamic programming","display_name":"On the connections between PCTL and dynamic programming","publication_year":2010,"publication_date":"2010-04-12","ids":{"openalex":"https://openalex.org/W2135245897","doi":"https://doi.org/10.1145/1755952.1755988","mag":"2135245897"},"language":"en","primary_location":{"id":"doi:10.1145/1755952.1755988","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1755952.1755988","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 13th ACM international conference on Hybrid systems: computation and control","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0910.4738","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039086017","display_name":"Federico Ramponi","orcid":"https://orcid.org/0000-0002-8036-6947"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Federico Ramponi","raw_affiliation_strings":["ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011060717","display_name":"Debasish Chatterjee","orcid":"https://orcid.org/0000-0002-1718-653X"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Debasish Chatterjee","raw_affiliation_strings":["ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038655214","display_name":"Sean Summers","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Sean Summers","raw_affiliation_strings":["ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007359599","display_name":"John Lygeros","orcid":"https://orcid.org/0000-0002-6159-1962"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"John Lygeros","raw_affiliation_strings":["ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.5579,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.97692734,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"253","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6551544070243835},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6464471220970154},{"id":"https://openalex.org/keywords/modal-logic","display_name":"Modal logic","score":0.6303321123123169},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6147735118865967},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.6028331518173218},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.5756494998931885},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5439867377281189},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.5194249153137207},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5174716114997864},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4809681475162506},{"id":"https://openalex.org/keywords/probabilistic-ctl","display_name":"Probabilistic CTL","score":0.46680429577827454},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.392857164144516},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.3609299659729004},{"id":"https://openalex.org/keywords/modal","display_name":"Modal","score":0.35361170768737793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3352137804031372},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31393471360206604},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0776839554309845},{"id":"https://openalex.org/keywords/probabilistic-analysis-of-algorithms","display_name":"Probabilistic analysis of algorithms","score":0.06572556495666504}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6551544070243835},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6464471220970154},{"id":"https://openalex.org/C27508121","wikidata":"https://www.wikidata.org/wiki/Q210841","display_name":"Modal logic","level":3,"score":0.6303321123123169},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6147735118865967},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.6028331518173218},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.5756494998931885},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5439867377281189},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.5194249153137207},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5174716114997864},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4809681475162506},{"id":"https://openalex.org/C52063229","wikidata":"https://www.wikidata.org/wiki/Q7246845","display_name":"Probabilistic CTL","level":4,"score":0.46680429577827454},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.392857164144516},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.3609299659729004},{"id":"https://openalex.org/C71139939","wikidata":"https://www.wikidata.org/wiki/Q910194","display_name":"Modal","level":2,"score":0.35361170768737793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3352137804031372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31393471360206604},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0776839554309845},{"id":"https://openalex.org/C24404364","wikidata":"https://www.wikidata.org/wiki/Q7246846","display_name":"Probabilistic analysis of algorithms","level":3,"score":0.06572556495666504},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1755952.1755988","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1755952.1755988","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 13th ACM international conference on Hybrid systems: computation and control","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:0910.4738","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0910.4738","pdf_url":"https://arxiv.org/pdf/0910.4738","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.766.6455","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.766.6455","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0910.4738.pdf","raw_type":"text"},{"id":"pmh:oai:iris.unibs.it:11379/132122","is_oa":false,"landing_page_url":"http://hdl.handle.net/11379/132122","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/bookPart"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0910.4738","is_oa":true,"landing_page_url":"https://arxiv.org/abs/0910.4738","pdf_url":"https://arxiv.org/pdf/0910.4738","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2696256921","display_name":null,"funder_award_id":"200021-122072","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5006253497","display_name":"Stochastic Model Predictive Control","funder_award_id":"122072","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5256785375","display_name":null,"funder_award_id":"200021-","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2135245897.pdf","grobid_xml":"https://content.openalex.org/works/W2135245897.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W100327610","https://openalex.org/W1489501223","https://openalex.org/W1516256348","https://openalex.org/W1575802629","https://openalex.org/W1576452626","https://openalex.org/W1586486602","https://openalex.org/W1850048324","https://openalex.org/W1859458367","https://openalex.org/W1865728679","https://openalex.org/W1882576690","https://openalex.org/W1967954124","https://openalex.org/W1968933618","https://openalex.org/W1998980567","https://openalex.org/W2005998857","https://openalex.org/W2010654234","https://openalex.org/W2012270151","https://openalex.org/W2013614847","https://openalex.org/W2029308352","https://openalex.org/W2047343396","https://openalex.org/W2056987876","https://openalex.org/W2080813827","https://openalex.org/W2085380472","https://openalex.org/W2086005600","https://openalex.org/W2090501324","https://openalex.org/W2092008396","https://openalex.org/W2097415784","https://openalex.org/W2098432798","https://openalex.org/W2114489703","https://openalex.org/W2118039525","https://openalex.org/W2122087968","https://openalex.org/W2122407545","https://openalex.org/W2124446794","https://openalex.org/W2125845083","https://openalex.org/W2135832649","https://openalex.org/W2138826199","https://openalex.org/W2140646474","https://openalex.org/W2150882248","https://openalex.org/W2159650620","https://openalex.org/W2160516500","https://openalex.org/W2162861715","https://openalex.org/W2164096878","https://openalex.org/W2214757433","https://openalex.org/W2316812274","https://openalex.org/W2400458653","https://openalex.org/W2487144912","https://openalex.org/W2595897327","https://openalex.org/W2612952478","https://openalex.org/W2765542298","https://openalex.org/W2798461040","https://openalex.org/W3105022375","https://openalex.org/W4206751862","https://openalex.org/W4238339534","https://openalex.org/W4249676319","https://openalex.org/W4253201987","https://openalex.org/W4298084067"],"related_works":["https://openalex.org/W2168246878","https://openalex.org/W4213436577","https://openalex.org/W2401977081","https://openalex.org/W1572578464","https://openalex.org/W4214926706","https://openalex.org/W2403555318","https://openalex.org/W4388236136","https://openalex.org/W2804745155","https://openalex.org/W2807018115","https://openalex.org/W925418074"],"abstract_inverted_index":{"Probabilistic":[0],"Computation":[1],"Tree":[2],"Logic":[3],"(PCTL)":[4],"is":[5,45],"a":[6,13,46],"well-known":[7],"modal":[8],"logic":[9],"which":[10,83],"has":[11],"become":[12],"standard":[14],"for":[15,36],"expressing":[16],"temporal":[17],"properties":[18,63],"of":[19,26,51,56,64,96],"finite-state":[20],"Markov":[21,38],"chains":[22],"in":[23,80],"the":[24,65,68],"context":[25],"automated":[27],"model":[28],"checking.":[29],"In":[30],"this":[31],"paper,":[32],"we":[33,41],"consider":[34],"PCTL":[35,97],"noncountable-space":[37],"chains,":[39],"and":[40,54,75],"show":[42],"that":[43],"there":[44],"substantial":[47],"affinity":[48],"between":[49],"certain":[50],"its":[52],"operators":[53],"problems":[55],"Dynamic":[57],"Programming.":[58],"We":[59,70],"prove":[60],"some":[61],"basic":[62],"solutions":[66],"to":[67],"latter.":[69],"also":[71],"provide":[72],"two":[73],"examples":[74],"demonstrate":[76],"how":[77],"recovery":[78],"strategies":[79],"practical":[81],"applications,":[82],"are":[84],"naturally":[85],"stated":[86],"as":[87,93],"reach-avoid":[88],"problems,":[89],"can":[90],"be":[91],"viewed":[92],"particular":[94],"cases":[95],"formulas.":[98]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}