{"id":"https://openalex.org/W3196583636","doi":"https://doi.org/10.1007/978-3-030-89716-1_10","title":"Reachability is NP-Complete Even for the Simplest Neural Networks","display_name":"Reachability is NP-Complete Even for the Simplest Neural Networks","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3196583636","doi":"https://doi.org/10.1007/978-3-030-89716-1_10","mag":"3196583636"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-030-89716-1_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-89716-1_10","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://export.arxiv.org/pdf/2108.13179","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019371898","display_name":"Marco S\u00e4lzer","orcid":"https://orcid.org/0000-0002-8012-5465"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Marco S\u00e4lzer","raw_affiliation_strings":["School of Electr. Eng. and Computer Science, University of Kassel, Kassel, Germany","University of Kassel"],"raw_orcid":"https://orcid.org/0000-0002-8012-5465","affiliations":[{"raw_affiliation_string":"School of Electr. Eng. and Computer Science, University of Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]},{"raw_affiliation_string":"University of Kassel","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087768042","display_name":"Martin Lange","orcid":"https://orcid.org/0000-0002-1621-0972"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Lange","raw_affiliation_strings":["School of Electr. Eng. and Computer Science, University of Kassel, Kassel, Germany","University of Kassel"],"raw_orcid":"https://orcid.org/0000-0002-1621-0972","affiliations":[{"raw_affiliation_string":"School of Electr. Eng. and Computer Science, University of Kassel, Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]},{"raw_affiliation_string":"University of Kassel","institution_ids":["https://openalex.org/I106157433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019371898"],"corresponding_institution_ids":["https://openalex.org/I106157433"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16748768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"149","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":1.0,"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":1.0,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9970999956130981,"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/reachability","display_name":"Reachability","score":0.9265245199203491},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7471517324447632},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7364763021469116},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6982702016830444},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6001924872398376},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5877291560173035},{"id":"https://openalex.org/keywords/reachability-problem","display_name":"Reachability problem","score":0.5156592130661011},{"id":"https://openalex.org/keywords/deep-neural-networks","display_name":"Deep neural networks","score":0.501370906829834},{"id":"https://openalex.org/keywords/layer","display_name":"Layer (electronics)","score":0.42058634757995605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31861042976379395},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.31543999910354614},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2351660430431366},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05181893706321716}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9265245199203491},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7471517324447632},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7364763021469116},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6982702016830444},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6001924872398376},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5877291560173035},{"id":"https://openalex.org/C2777669093","wikidata":"https://www.wikidata.org/wiki/Q17141570","display_name":"Reachability problem","level":3,"score":0.5156592130661011},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.501370906829834},{"id":"https://openalex.org/C2779227376","wikidata":"https://www.wikidata.org/wiki/Q6505497","display_name":"Layer (electronics)","level":2,"score":0.42058634757995605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31861042976379395},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.31543999910354614},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2351660430431366},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05181893706321716},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-030-89716-1_10","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-030-89716-1_10","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"mag:3196583636","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2108.13179","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2108.13179","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2108.13179","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"mag:3196583636","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2108.13179","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W2160815625","https://openalex.org/W2592929672","https://openalex.org/W2594877703","https://openalex.org/W2611147814","https://openalex.org/W2618530766","https://openalex.org/W2800473699","https://openalex.org/W2801079363","https://openalex.org/W2910121883","https://openalex.org/W2963054787","https://openalex.org/W2963673089","https://openalex.org/W2981207549","https://openalex.org/W3036286896","https://openalex.org/W3100321043","https://openalex.org/W3124849400","https://openalex.org/W3190946860"],"related_works":["https://openalex.org/W3082719733","https://openalex.org/W1514329432","https://openalex.org/W3026837710","https://openalex.org/W2142565884","https://openalex.org/W1668734676","https://openalex.org/W1587797581","https://openalex.org/W1981914472","https://openalex.org/W2123776260","https://openalex.org/W150847977","https://openalex.org/W2096200279","https://openalex.org/W2020889012","https://openalex.org/W2002616520","https://openalex.org/W1885150995","https://openalex.org/W1536765582","https://openalex.org/W2142612879","https://openalex.org/W1599271043","https://openalex.org/W1605779591","https://openalex.org/W2282453390","https://openalex.org/W2152058358","https://openalex.org/W3104027319"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
