{"id":"https://openalex.org/W4311354561","doi":"https://doi.org/10.1007/s10009-022-00685-9","title":"Analyzing neural network behavior through deep statistical model checking","display_name":"Analyzing neural network behavior through deep statistical model checking","publication_year":2022,"publication_date":"2022-12-13","ids":{"openalex":"https://openalex.org/W4311354561","doi":"https://doi.org/10.1007/s10009-022-00685-9"},"language":"en","primary_location":{"id":"doi:10.1007/s10009-022-00685-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10009-022-00685-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10009-022-00685-9.pdf","source":{"id":"https://openalex.org/S122567160","display_name":"International Journal on Software Tools for Technology Transfer","issn_l":"1433-2779","issn":["1433-2779","1433-2787"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal on Software Tools for Technology Transfer","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10009-022-00685-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033310691","display_name":"Timo P. Gros","orcid":"https://orcid.org/0000-0002-1100-1952"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Timo P. Gros","raw_affiliation_strings":["Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028747794","display_name":"Holger Hermanns","orcid":"https://orcid.org/0000-0002-2766-9615"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Holger Hermanns","raw_affiliation_strings":["Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076532681","display_name":"J\u00f6rg Hoffmann","orcid":"https://orcid.org/0000-0003-1590-5876"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Hoffmann","raw_affiliation_strings":["Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023667141","display_name":"Michaela Klauck","orcid":"https://orcid.org/0000-0002-6353-227X"},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Michaela Klauck","raw_affiliation_strings":["Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009995873","display_name":"Marcel Steinmetz","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marcel Steinmetz","raw_affiliation_strings":["Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Saarland Informatics Campus, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009995873","https://openalex.org/A5023667141","https://openalex.org/A5028747794","https://openalex.org/A5033310691","https://openalex.org/A5076532681"],"corresponding_institution_ids":["https://openalex.org/I91712215"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":1.045,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80191447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"25","issue":"3","first_page":"407","last_page":"426"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9894999861717224,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.9894999861717224,"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":0.8687775135040283},{"id":"https://openalex.org/keywords/model-checking","display_name":"Model checking","score":0.7298728227615356},{"id":"https://openalex.org/keywords/markov-decision-process","display_name":"Markov decision process","score":0.6053213477134705},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5643779635429382},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5220082402229309},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4739953279495239},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.45274314284324646},{"id":"https://openalex.org/keywords/testbed","display_name":"Testbed","score":0.44667574763298035},{"id":"https://openalex.org/keywords/formal-verification","display_name":"Formal verification","score":0.41630876064300537},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.34781181812286377},{"id":"https://openalex.org/keywords/markov-process","display_name":"Markov process","score":0.23160171508789062}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8687775135040283},{"id":"https://openalex.org/C110251889","wikidata":"https://www.wikidata.org/wiki/Q1569697","display_name":"Model checking","level":2,"score":0.7298728227615356},{"id":"https://openalex.org/C106189395","wikidata":"https://www.wikidata.org/wiki/Q176789","display_name":"Markov decision process","level":3,"score":0.6053213477134705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5643779635429382},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5220082402229309},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4739953279495239},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.45274314284324646},{"id":"https://openalex.org/C31395832","wikidata":"https://www.wikidata.org/wiki/Q1318674","display_name":"Testbed","level":2,"score":0.44667574763298035},{"id":"https://openalex.org/C111498074","wikidata":"https://www.wikidata.org/wiki/Q173326","display_name":"Formal verification","level":2,"score":0.41630876064300537},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34781181812286377},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.23160171508789062},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10009-022-00685-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10009-022-00685-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10009-022-00685-9.pdf","source":{"id":"https://openalex.org/S122567160","display_name":"International Journal on Software Tools for Technology Transfer","issn_l":"1433-2779","issn":["1433-2779","1433-2787"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal on Software Tools for Technology Transfer","raw_type":"journal-article"},{"id":"pmh:oai:publikationen.sulb.uni-saarland.de:20.500.11880/34956","is_oa":true,"landing_page_url":"http://dx.doi.org/10.22028/D291-38784","pdf_url":null,"source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doc-type:article"},{"id":"doi:10.22028/d291-38784","is_oa":true,"landing_page_url":"https://doi.org/10.22028/d291-38784","pdf_url":null,"source":{"id":"https://openalex.org/S4377196499","display_name":"Publications of the UdS (Saarland University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I91712215","host_organization_name":"Saarland University","host_organization_lineage":["https://openalex.org/I91712215"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Collection"}],"best_oa_location":{"id":"doi:10.1007/s10009-022-00685-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10009-022-00685-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10009-022-00685-9.pdf","source":{"id":"https://openalex.org/S122567160","display_name":"International Journal on Software Tools for Technology Transfer","issn_l":"1433-2779","issn":["1433-2779","1433-2787"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal on Software Tools for Technology Transfer","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7900000214576721,"display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G3032849772","display_name":null,"funder_award_id":"TRR 248","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G890954746","display_name":"TRR 248: Grundlagen verst\u00e4ndlicher SoftwareSysteme  f\u00fcr eine nachvollziehbare cyberphysische Welt","funder_award_id":"389792660","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320323322","display_name":"Universit\u00e4t des Saarlandes","ror":"https://ror.org/01jdpyv68"},{"id":"https://openalex.org/F4320324004","display_name":"Forskningsr\u00e5det om H\u00e4lsa, Arbetsliv och V\u00e4lf\u00e4rd","ror":"https://ror.org/02d290r06"},{"id":"https://openalex.org/F4320335322","display_name":"European Regional Development Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4311354561.pdf","grobid_xml":"https://content.openalex.org/works/W4311354561.grobid-xml"},"referenced_works_count":59,"referenced_works":["https://openalex.org/W275084143","https://openalex.org/W296769721","https://openalex.org/W1489725951","https://openalex.org/W1499021164","https://openalex.org/W1516256348","https://openalex.org/W1544634046","https://openalex.org/W1617322827","https://openalex.org/W1862398452","https://openalex.org/W1976268573","https://openalex.org/W1977177161","https://openalex.org/W2005998857","https://openalex.org/W2009533501","https://openalex.org/W2018000058","https://openalex.org/W2114710208","https://openalex.org/W2137983211","https://openalex.org/W2145339207","https://openalex.org/W2160815625","https://openalex.org/W2177617373","https://openalex.org/W2222789563","https://openalex.org/W2334782222","https://openalex.org/W2403355785","https://openalex.org/W2482035342","https://openalex.org/W2543296129","https://openalex.org/W2593267253","https://openalex.org/W2594877703","https://openalex.org/W2598014203","https://openalex.org/W2776485332","https://openalex.org/W2794609696","https://openalex.org/W2797945469","https://openalex.org/W2810147724","https://openalex.org/W2902907165","https://openalex.org/W2905299363","https://openalex.org/W2912198824","https://openalex.org/W2917325587","https://openalex.org/W2932972683","https://openalex.org/W2954207605","https://openalex.org/W2960567166","https://openalex.org/W2962295100","https://openalex.org/W2963054787","https://openalex.org/W2963208512","https://openalex.org/W2966504041","https://openalex.org/W2979249584","https://openalex.org/W2981639301","https://openalex.org/W2981739602","https://openalex.org/W3035170447","https://openalex.org/W3095326590","https://openalex.org/W3096351713","https://openalex.org/W3103644807","https://openalex.org/W3124416149","https://openalex.org/W3155039249","https://openalex.org/W3185700666","https://openalex.org/W3194575292","https://openalex.org/W3198534868","https://openalex.org/W4230704549","https://openalex.org/W4237868629","https://openalex.org/W4283802686","https://openalex.org/W4290052206","https://openalex.org/W4317826956","https://openalex.org/W4394050915"],"related_works":["https://openalex.org/W2117798332","https://openalex.org/W2177212599","https://openalex.org/W2115279934","https://openalex.org/W1503071078","https://openalex.org/W1998949669","https://openalex.org/W1558598345","https://openalex.org/W3158759410","https://openalex.org/W2151898527","https://openalex.org/W4289687320","https://openalex.org/W2106934209"],"abstract_inverted_index":{"Abstract":[0],"Neural":[1],"networks":[2],"(NN)":[3],"are":[4,20],"taking":[5],"over":[6],"ever":[7],"more":[8],"decisions":[9],"thus":[10],"far":[11,21],"taken":[12],"by":[13,220],"humans,":[14],"even":[15,34],"though":[16],"verifiable":[17],"system-level":[18],"guarantees":[19],"out":[22],"of":[23,68,75,92,143,163,189,237,252,257,268,279],"reach.":[24],"Neither":[25],"is":[26,32,54,155,173,204,211],"the":[27,61,90,97,104,125,132,135,144,146,170,205,212,216,223,230,240,250,258,277],"verification":[28,117,133],"technology":[29],"available,":[30],"nor":[31],"it":[33,193],"understood":[35],"what":[36,176],"a":[37,49,66,111,141,149,186,266],"formal,":[38],"meaningful,":[39],"extensible,":[40],"and":[41,79,166,261],"scalable":[42],"testbed":[43],"might":[44],"look":[45],"like":[46,201,276],"for":[47],"such":[48,154],"technology.":[50],"The":[51,119,161],"present":[52,65],"paper":[53],"an":[55,164,167,235],"attempt":[56],"to":[57,96,99,127,157,175,195,215],"improve":[58,229],"on":[59,234,254],"both":[60],"above":[62],"aspects.":[63],"We":[64,232],"family":[67],"formal":[69],"models":[70],"that":[71],"contain":[72],"basic":[73],"features":[74],"automated":[76],"decision-making":[77],"contexts":[78],"which":[80,152],"can":[81],"be":[82],"extended":[83],"with":[84,245],"further":[85,227],"orthogonal":[86],"features,":[87],"ultimately":[88],"encompassing":[89],"scope":[91],"autonomous":[93],"driving.":[94],"Due":[95],"possibility":[98],"model":[100,108,159,181,191,221,259],"random":[101],"noise":[102],"in":[103,121,243],"decision":[105,113],"actuation,":[106],"each":[107],"instance":[109,269],"induces":[110],"Markov":[112,150],"process":[114],"(MDP)":[115],"as":[116,140,153,265,271,273],"object.":[118],"NN":[120,138,168,213,280],"this":[122],"context":[123],"has":[124],"duty":[126],"actuate":[128],"(near-optimal)":[129],"decisions.":[130],"From":[131],"perspective,":[134],"externally":[136,246],"learnt":[137,247],"serves":[139],"determinizer":[142],"MDP,":[145],"result":[147],"being":[148,185],"chain":[151],"amenable":[156],"statistical":[158,180,190],"checking.":[160],"combination":[162,244],"MDP":[165],"encoding":[169],"action":[171],"policy":[172],"central":[174],"we":[177],"call":[178],"\u201cdeep":[179],"checking\u201d":[182],"(DSMC).":[183],"While":[184],"straightforward":[187],"extension":[188],"checking,":[192],"enables":[194],"gain":[196],"deep":[197],"insight":[198],"into":[199],"questions":[200],"\u201chow":[202,209],"high":[203],"NN-induced":[206],"safety":[207],"risk?\u201d,":[208],"good":[210],"compared":[214],"optimal":[217],"policy?\u201d":[218],"(obtained":[219],"checking":[222],"MDP),":[224],"or":[225],"\u201cdoes":[226],"training":[228],"NN?\u201d.":[231],"report":[233],"implementation":[236],"DSMC":[238,253],"inside":[239],"Modest":[241],"Toolset":[242],"NNs,":[248],"demonstrating":[249],"potential":[251],"various":[255],"instances":[256],"family,":[260],"illustrating":[262],"its":[263],"scalability":[264],"function":[267],"size":[270],"well":[272],"other":[274],"factors":[275],"degree":[278],"training.":[281]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3}],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-10T00:00:00"}