{"id":"https://openalex.org/W4384471541","doi":"https://doi.org/10.1007/978-3-031-37709-9_5","title":"MDPs as\u00a0Distribution Transformers: Affine Invariant Synthesis for\u00a0Safety Objectives","display_name":"MDPs as\u00a0Distribution Transformers: Affine Invariant Synthesis for\u00a0Safety Objectives","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4384471541","doi":"https://doi.org/10.1007/978-3-031-37709-9_5"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-37709-9_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_5.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063753055","display_name":"S. Akshay","orcid":null},"institutions":[{"id":"https://openalex.org/I162827531","display_name":"Indian Institute of Technology Bombay","ror":"https://ror.org/02qyf5152","country_code":"IN","type":"education","lineage":["https://openalex.org/I162827531"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"S. Akshay","raw_affiliation_strings":["Indian Institute of Technology Bombay, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Indian Institute of Technology Bombay, Mumbai, India","institution_ids":["https://openalex.org/I162827531"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052607806","display_name":"Krishnendu Chatterjee","orcid":"https://orcid.org/0000-0002-4561-241X"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Krishnendu Chatterjee","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023690820","display_name":"Tobias Meggendorfer","orcid":"https://orcid.org/0000-0002-1712-2165"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]},{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["AT","DE"],"is_corresponding":false,"raw_author_name":"Tobias Meggendorfer","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","Technical University of Munich, Munich, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]},{"raw_affiliation_string":"Technical University of Munich, Munich, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041082080","display_name":"\u0110or\u0111e \u017dikeli\u0107","orcid":"https://orcid.org/0000-0002-4681-1699"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"\u0110or\u0111e \u017dikeli\u0107","raw_affiliation_strings":["Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria"],"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (ISTA), Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063753055"],"corresponding_institution_ids":["https://openalex.org/I162827531"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":{"value":5000,"currency":"EUR","value_usd":5392},"fwci":0.9864,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76196709,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"86","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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":0.9995999932289124,"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/T12423","display_name":"Software Reliability and Analysis Research","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1712","display_name":"Software"},"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/T13295","display_name":"Safety Systems Engineering in Autonomy","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.8067735433578491},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.8053076267242432},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5572277307510376},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.49955129623413086},{"id":"https://openalex.org/keywords/transformer","display_name":"Transformer","score":0.4632396101951599},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4378894567489624},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4237965941429138},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36067861318588257},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35583633184432983},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.23474308848381042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.14299869537353516}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8067735433578491},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.8053076267242432},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5572277307510376},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.49955129623413086},{"id":"https://openalex.org/C66322947","wikidata":"https://www.wikidata.org/wiki/Q11658","display_name":"Transformer","level":3,"score":0.4632396101951599},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4378894567489624},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4237965941429138},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36067861318588257},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35583633184432983},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.23474308848381042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.14299869537353516},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-031-37709-9_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_5.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-3-031-37709-9_5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-3-031-37709-9_5","pdf_url":"https://link.springer.com/content/pdf/10.1007/978-3-031-37709-9_5.pdf","source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.5600000023841858,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G1762991518","display_name":null,"funder_award_id":"EP/V00252X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1974542962","display_name":null,"funder_award_id":"Sk\u0142odowska","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2013768499","display_name":null,"funder_award_id":"665385","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2689612763","display_name":null,"funder_award_id":"Marie","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4956428346","display_name":null,"funder_award_id":"Horizon 2020 research and innovatio","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5036817778","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innov","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7282925181","display_name":"Formal Methods for Stochastic Models: Algorithms and Applications","funder_award_id":"863818","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8051717526","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8318064016","display_name":null,"funder_award_id":"Horizon","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G8633428685","display_name":null,"funder_award_id":"European Union's Horizon 2020 research and innovat","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320313934","display_name":"Institut national de recherche en informatique et en automatique (INRIA)","ror":"https://ror.org/02kvxyf05"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320321027","display_name":"Indo-French Centre for the Promotion of Advanced Research","ror":"https://ror.org/017aem598"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334771","display_name":"Science and Engineering Research Board","ror":"https://ror.org/03ffdsr55"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4384471541.pdf"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W12758337","https://openalex.org/W72346910","https://openalex.org/W87140126","https://openalex.org/W145069693","https://openalex.org/W221832247","https://openalex.org/W287611495","https://openalex.org/W1480909796","https://openalex.org/W1498432697","https://openalex.org/W1505135855","https://openalex.org/W1523037784","https://openalex.org/W1526922602","https://openalex.org/W1530375435","https://openalex.org/W1563374593","https://openalex.org/W1585038871","https://openalex.org/W1608799719","https://openalex.org/W1611084195","https://openalex.org/W1734364899","https://openalex.org/W1797219784","https://openalex.org/W1982800675","https://openalex.org/W2020997970","https://openalex.org/W2021112905","https://openalex.org/W2035537281","https://openalex.org/W2037009101","https://openalex.org/W2043100293","https://openalex.org/W2058033966","https://openalex.org/W2067754486","https://openalex.org/W2073629816","https://openalex.org/W2099629271","https://openalex.org/W2104835568","https://openalex.org/W2114554615","https://openalex.org/W2135706240","https://openalex.org/W2141289380","https://openalex.org/W2141670510","https://openalex.org/W2185676247","https://openalex.org/W2209422068","https://openalex.org/W2334782222","https://openalex.org/W2398327122","https://openalex.org/W2417863416","https://openalex.org/W2435583538","https://openalex.org/W2548604229","https://openalex.org/W2625924363","https://openalex.org/W2755806184","https://openalex.org/W2780276625","https://openalex.org/W2807469900","https://openalex.org/W2893610333","https://openalex.org/W2914740438","https://openalex.org/W2963819197","https://openalex.org/W2964314311","https://openalex.org/W3033865919","https://openalex.org/W3166575995","https://openalex.org/W3171209508","https://openalex.org/W3176250057","https://openalex.org/W3186609013","https://openalex.org/W3189389740","https://openalex.org/W4255442211","https://openalex.org/W4281612951","https://openalex.org/W4281781753","https://openalex.org/W4283796290","https://openalex.org/W4302114916","https://openalex.org/W4313229213","https://openalex.org/W4366451130","https://openalex.org/W6812072083"],"related_works":["https://openalex.org/W2127267268","https://openalex.org/W2136512912","https://openalex.org/W2067910792","https://openalex.org/W2156446763","https://openalex.org/W2143461633","https://openalex.org/W2150194458","https://openalex.org/W4321471459","https://openalex.org/W2889071233","https://openalex.org/W2380814829","https://openalex.org/W2387511021"],"abstract_inverted_index":{"Abstract":[0],"Markov":[1],"decision":[2],"processes":[3],"can":[4,61,124,137,158],"be":[5,35],"viewed":[6],"as":[7,105],"transformers":[8],"of":[9,25,53,69,103,144],"probability":[10],"distributions.":[11],"While":[12],"this":[13,121],"view":[14],"is":[15,91,147],"useful":[16],"from":[17],"a":[18,73,85,97],"practical":[19],"standpoint":[20],"to":[21,34,40,77],"reason":[22],"about":[23],"trajectories":[24],"distributions,":[26],"basic":[27],"reachability":[28],"and":[29,65,108,154],"safety":[30,57,86,112],"problems":[31],"are":[32],"known":[33],"computationally":[36],"intractable":[37],"(i.e.,":[38],"Skolem-hard)":[39],"solve":[41,159],"in":[42,80,114,148],"such":[43,83],"models.":[44],"Further,":[45],"we":[46,71,95],"show":[47,155],"that":[48,84,156],"even":[49],"for":[50,56,100,111],"simple":[51],"examples":[52],"MDPs,":[54],"strategies":[55,79],"objectives":[58,113],"over":[59,88],"distributions":[60,90],"require":[62],"infinite":[63],"memory":[64],"randomization.":[66],"In":[67],"light":[68],"this,":[70],"present":[72],"novel":[74],"overapproximation":[75],"approach":[76],"synthesize":[78,126,138],"an":[81],"MDP,":[82],"objective":[87],"the":[89,135],"met.":[92],"More":[93],"precisely,":[94],"develop":[96],"new":[98],"framework":[99],"template-based":[101],"synthesis":[102],"certificates":[104],"affine":[106],"distributional":[107],"inductive":[109],"invariants":[110],"MDPs.":[115],"We":[116,150],"provide":[117],"two":[118],"algorithms":[119,146,153],"within":[120],"framework.":[122],"One":[123],"only":[125],"memoryless":[127],"strategies,":[128],"but":[129],"has":[130],"relative":[131],"completeness":[132],"guarantees,":[133],"while":[134],"other":[136],"general":[139],"strategies.":[140],"The":[141],"runtime":[142],"complexity":[143],"both":[145],"PSPACE.":[149],"implement":[151],"these":[152],"they":[157],"several":[160],"non-trivial":[161],"examples.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}