{"id":"https://openalex.org/W1570924439","doi":"https://doi.org/10.1007/3-540-60246-1_130","title":"Some typical properties of large AND/OR Boolean formulas","display_name":"Some typical properties of large AND/OR Boolean formulas","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1570924439","doi":"https://doi.org/10.1007/3-540-60246-1_130","mag":"1570924439"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-60246-1_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-60246-1_130","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/A5111723650","display_name":"Hanno Lefmann","orcid":null},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"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":["CZ","DE"],"is_corresponding":true,"raw_author_name":"Hanno Lefmann","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of Czech Republic, Prague, Czech Republic","Lehrstuhl Informatik II, Universit\u00e4t Dortmund, D-44221, Dortmund, Germany","Academy of Sciences of Czech Republic","Universit\u00e4t Dortmund"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of Czech Republic, Prague, Czech Republic","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Lehrstuhl Informatik II, Universit\u00e4t Dortmund, D-44221, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Academy of Sciences of Czech Republic","institution_ids":["https://openalex.org/I202391551"]},{"raw_affiliation_string":"Universit\u00e4t Dortmund","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060114081","display_name":"Petr Savick\u00fd","orcid":"https://orcid.org/0000-0001-6974-0718"},"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"]},{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"funder","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210155092","display_name":"Czech Academy of Sciences, Institute of Computer Science","ror":"https://ror.org/0496n6574","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]}],"countries":["CZ","DE"],"is_corresponding":false,"raw_author_name":"Petr Savick\u00fd","raw_affiliation_strings":["Institute of Computer Science, Academy of Sciences of Czech Republic, Prague, Czech Republic","Lehrstuhl Informatik II, Universit\u00e4t Dortmund, D-44221, Dortmund, Germany","Academy of Sciences of Czech Republic","Universit\u00e4t Dortmund"],"affiliations":[{"raw_affiliation_string":"Institute of Computer Science, Academy of Sciences of Czech Republic, Prague, Czech Republic","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210155092"]},{"raw_affiliation_string":"Lehrstuhl Informatik II, Universit\u00e4t Dortmund, D-44221, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Academy of Sciences of Czech Republic","institution_ids":["https://openalex.org/I202391551"]},{"raw_affiliation_string":"Universit\u00e4t Dortmund","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111723650"],"corresponding_institution_ids":["https://openalex.org/I200332995","https://openalex.org/I202391551","https://openalex.org/I4210155092"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.17186761,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"237","last_page":"246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9980000257492065,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.7078801989555359},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6967427134513855},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.641268789768219},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.5476058125495911},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.5472171306610107},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5457963943481445},{"id":"https://openalex.org/keywords/binary-tree","display_name":"Binary tree","score":0.5351536870002747},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5259509086608887},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5210344791412354},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5160753130912781},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4815795421600342},{"id":"https://openalex.org/keywords/boolean-model","display_name":"Boolean model","score":0.4760948419570923},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.4740198254585266},{"id":"https://openalex.org/keywords/uniform-distribution","display_name":"Uniform distribution (continuous)","score":0.46897944808006287},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.46104925870895386},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.426360547542572},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.423200786113739},{"id":"https://openalex.org/keywords/binary-decision-diagram","display_name":"Binary decision diagram","score":0.41873592138290405},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.39337363839149475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20601239800453186},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.15601429343223572},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11861580610275269},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10090869665145874},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09718483686447144}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7078801989555359},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6967427134513855},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.641268789768219},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.5476058125495911},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.5472171306610107},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5457963943481445},{"id":"https://openalex.org/C197855036","wikidata":"https://www.wikidata.org/wiki/Q380172","display_name":"Binary tree","level":2,"score":0.5351536870002747},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5259509086608887},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5210344791412354},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5160753130912781},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4815795421600342},{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.4760948419570923},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.4740198254585266},{"id":"https://openalex.org/C108882938","wikidata":"https://www.wikidata.org/wiki/Q274506","display_name":"Uniform distribution (continuous)","level":2,"score":0.46897944808006287},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.46104925870895386},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.426360547542572},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.423200786113739},{"id":"https://openalex.org/C3309909","wikidata":"https://www.wikidata.org/wiki/Q864155","display_name":"Binary decision diagram","level":2,"score":0.41873592138290405},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.39337363839149475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20601239800453186},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.15601429343223572},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11861580610275269},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10090869665145874},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09718483686447144},{"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/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/3-540-60246-1_130","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-60246-1_130","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:CiteSeerX.psu:10.1.1.47.1791","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.1791","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.uivt.cas.cz/vvvvedci/savicky/papers/andor.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1568586753","https://openalex.org/W1984843325","https://openalex.org/W2008470071","https://openalex.org/W2064556108","https://openalex.org/W2089842783","https://openalex.org/W2135251664","https://openalex.org/W2145818164"],"related_works":["https://openalex.org/W1499231756","https://openalex.org/W47695625","https://openalex.org/W4243283211","https://openalex.org/W1979032657","https://openalex.org/W2940617399","https://openalex.org/W98542587","https://openalex.org/W4390143711","https://openalex.org/W2044916592","https://openalex.org/W2952996136","https://openalex.org/W3004804172"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}