{"id":"https://openalex.org/W1547270959","doi":"https://doi.org/10.1007/3-540-59042-0_64","title":"On realizing iterated multiplication by small depth threshold circuits","display_name":"On realizing iterated multiplication by small depth threshold circuits","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1547270959","doi":"https://doi.org/10.1007/3-540-59042-0_64","mag":"1547270959"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-59042-0_64","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59042-0_64","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":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088337575","display_name":"Matthias Krause","orcid":"https://orcid.org/0000-0002-3200-3199"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Krause","raw_affiliation_strings":["Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Deutschland","Universit\u00e4t Dortmund"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Deutschland","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Universit\u00e4t Dortmund","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088337575"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.1082,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7519833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"83","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9976999759674072,"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/multiplication","display_name":"Multiplication (music)","score":0.8646371364593506},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.81193608045578},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6621366739273071},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5738780498504639},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.550689697265625},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5187152028083801},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4905056357383728},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47287270426750183},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.46563687920570374},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4635988771915436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3375973105430603},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17054280638694763},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.07358065247535706}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.8646371364593506},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.81193608045578},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6621366739273071},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5738780498504639},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.550689697265625},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5187152028083801},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4905056357383728},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47287270426750183},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.46563687920570374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4635988771915436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3375973105430603},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17054280638694763},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.07358065247535706},{"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-59042-0_64","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-59042-0_64","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":"pmh:oai:ub-madoc.bib.uni-mannheim.de:59769","is_oa":false,"landing_page_url":"https://link.springer.com/chapter/10.1007/3-540-59042-0_64","pdf_url":null,"source":{"id":"https://openalex.org/S4377196315","display_name":"MADOC (University of Mannheim)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177802217","host_organization_name":"University of Mannheim","host_organization_lineage":["https://openalex.org/I177802217"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Konferenzver\u00f6ffentlichung"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1556442495","https://openalex.org/W2014593388","https://openalex.org/W2055350589","https://openalex.org/W2062929592","https://openalex.org/W2071020383","https://openalex.org/W2071732851","https://openalex.org/W2088543905","https://openalex.org/W2097575812","https://openalex.org/W2097886040","https://openalex.org/W2101069215","https://openalex.org/W2114527013","https://openalex.org/W2116794057","https://openalex.org/W2129774539","https://openalex.org/W2139224092","https://openalex.org/W2185585538"],"related_works":["https://openalex.org/W2038759377","https://openalex.org/W3093500249","https://openalex.org/W3094080891","https://openalex.org/W2886205627","https://openalex.org/W2063343791","https://openalex.org/W2095090051","https://openalex.org/W1584559800","https://openalex.org/W2991811627","https://openalex.org/W1601569507","https://openalex.org/W1973045784"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-29T09:16:38.111599","created_date":"2025-10-10T00:00:00"}
