{"id":"https://openalex.org/W2142972886","doi":"https://doi.org/10.1145/2213977.2214030","title":"Polynomial time algorithms for multi-type branching processesand stochastic context-free grammars","display_name":"Polynomial time algorithms for multi-type branching processesand stochastic context-free grammars","publication_year":2012,"publication_date":"2012-05-19","ids":{"openalex":"https://openalex.org/W2142972886","doi":"https://doi.org/10.1145/2213977.2214030","mag":"2142972886"},"language":"en","primary_location":{"id":"doi:10.1145/2213977.2214030","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","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/A5003946901","display_name":"Kousha Etessami","orcid":"https://orcid.org/0000-0001-5700-3462"},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Kousha Etessami","raw_affiliation_strings":["University of Edinburgh, Edinburgh, United Kingdom","University of Edinburgh, edinburgh, United Kingdom"],"affiliations":[{"raw_affiliation_string":"University of Edinburgh, Edinburgh, United Kingdom","institution_ids":["https://openalex.org/I98677209"]},{"raw_affiliation_string":"University of Edinburgh, edinburgh, United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5106184727","display_name":"Alistair Stewart","orcid":null},"institutions":[{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alistair Stewart","raw_affiliation_strings":["School of Informatics, University of Edinburgh, United Kingdom"],"affiliations":[{"raw_affiliation_string":"School of Informatics, University of Edinburgh, United Kingdom","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043084405","display_name":"Mihalis Yannakakis","orcid":"https://orcid.org/0000-0003-2857-1860"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mihalis Yannakakis","raw_affiliation_strings":["Columbia University, New York, NY, USA"],"affiliations":[{"raw_affiliation_string":"Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003946901"],"corresponding_institution_ids":["https://openalex.org/I98677209"],"apc_list":null,"apc_paid":null,"fwci":9.8474,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.98103697,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"579","last_page":"588"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9997000098228455,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9959999918937683,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9890000224113464,"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/matrix-polynomial","display_name":"Matrix polynomial","score":0.567777693271637},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5655665993690491},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.5075794458389282},{"id":"https://openalex.org/keywords/square-free-polynomial","display_name":"Square-free polynomial","score":0.5065840482711792},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.47683635354042053},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4729982018470764},{"id":"https://openalex.org/keywords/branching","display_name":"Branching (polymer chemistry)","score":0.4711954593658447},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.46186333894729614},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.4570375680923462},{"id":"https://openalex.org/keywords/monic-polynomial","display_name":"Monic polynomial","score":0.45017361640930176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43752893805503845},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4050136208534241},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4040333926677704},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39099302887916565},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.3656657040119171},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08858773112297058},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08591139316558838},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06731921434402466}],"concepts":[{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.567777693271637},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5655665993690491},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5075794458389282},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.5065840482711792},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.47683635354042053},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4729982018470764},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.4711954593658447},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.46186333894729614},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.4570375680923462},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.45017361640930176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43752893805503845},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4050136208534241},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4040333926677704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39099302887916565},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3656657040119171},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08858773112297058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08591139316558838},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06731921434402466},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/2213977.2214030","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2214030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.ed.ac.uk:publications/98230091-3b83-4909-8657-8be1b7ba50a2","is_oa":false,"landing_page_url":"http://doi.acm.org/10.1145/2213977.2214030","pdf_url":null,"source":{"id":"https://openalex.org/S4406922455","display_name":"Edinburgh Research Explorer","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W32262330","https://openalex.org/W1256121109","https://openalex.org/W1493119321","https://openalex.org/W1496738390","https://openalex.org/W1500921805","https://openalex.org/W1523572153","https://openalex.org/W1549240140","https://openalex.org/W1559984321","https://openalex.org/W1574901103","https://openalex.org/W1966861855","https://openalex.org/W1978470410","https://openalex.org/W1991624978","https://openalex.org/W2002089154","https://openalex.org/W2005059149","https://openalex.org/W2009570821","https://openalex.org/W2010994761","https://openalex.org/W2023206235","https://openalex.org/W2040721698","https://openalex.org/W2101900268","https://openalex.org/W2107771181","https://openalex.org/W2117685302","https://openalex.org/W2117805292","https://openalex.org/W2133667894","https://openalex.org/W2142921329","https://openalex.org/W2142972886","https://openalex.org/W2148701797","https://openalex.org/W2167246417","https://openalex.org/W2293835388","https://openalex.org/W2568511220","https://openalex.org/W2610857016","https://openalex.org/W2798735774","https://openalex.org/W2951306656","https://openalex.org/W2964097106","https://openalex.org/W3099666054","https://openalex.org/W4231137976","https://openalex.org/W4232474943","https://openalex.org/W4235035462","https://openalex.org/W4235614310","https://openalex.org/W4247026961","https://openalex.org/W4256135625","https://openalex.org/W4285719527","https://openalex.org/W4297962570","https://openalex.org/W6697374374","https://openalex.org/W6750414328"],"related_works":["https://openalex.org/W2049824936","https://openalex.org/W1976750632","https://openalex.org/W2952764322","https://openalex.org/W4320339927","https://openalex.org/W2165697811","https://openalex.org/W2902965052","https://openalex.org/W4319599684","https://openalex.org/W4299962674","https://openalex.org/W2101109099","https://openalex.org/W2751514289"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"one":[3],"can":[4],"approximate":[5],"the":[6,25,29,39,45,52],"least":[7],"fixed":[8],"point":[9],"solution":[10],"for":[11],"a":[12],"multivariate":[13],"system":[14,30],"of":[15,28,31,44,49],"monotone":[16],"probabilistic":[17],"polynomial":[18,22],"equations":[19,32],"in":[20,23,34],"time":[21],"both":[24],"encoding":[26],"size":[27],"and":[33],"log(1/\u03b5),":[35],"where":[36],"\u03b5>0":[37],"is":[38,51],"desired":[40],"additive":[41],"error":[42],"bound":[43],"solution.":[46],"(The":[47],"model":[48],"computation":[50],"standard":[53],"Turing":[54],"machine":[55],"model.)":[56]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}