{"id":"https://openalex.org/W2754087920","doi":"https://doi.org/10.4230/lipics.fsttcs.2018.6","title":"Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees","display_name":"Quasi-polynomial Hitting Sets for Circuits with Restricted Parse Trees","publication_year":2017,"publication_date":"2017-09-10","ids":{"openalex":"https://openalex.org/W2754087920","doi":"https://doi.org/10.4230/lipics.fsttcs.2018.6","mag":"2754087920"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9905","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.6","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070371254","display_name":"Ramprasad Saptharishi","orcid":"https://orcid.org/0000-0002-7485-3220"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Saptharishi, Ramprasad","raw_affiliation_strings":["Tata Institute of Fundamental Research, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081157963","display_name":"Anamay Tengse","orcid":"https://orcid.org/0000-0002-7305-8110"},"institutions":[{"id":"https://openalex.org/I11947397","display_name":"Tata Institute of Fundamental Research","ror":"https://ror.org/03ht1xw27","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Tengse, Anamay","raw_affiliation_strings":["Tata Institute of Fundamental Research, Mumbai, India"],"affiliations":[{"raw_affiliation_string":"Tata Institute of Fundamental Research, Mumbai, India","institution_ids":["https://openalex.org/I11947397"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070371254"],"corresponding_institution_ids":["https://openalex.org/I11947397"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.15694405,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","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/T11435","display_name":"Polynomial and algebraic computation","score":0.9968000054359436,"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/electronic-circuit","display_name":"Electronic circuit","score":0.6185356378555298},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5739428997039795},{"id":"https://openalex.org/keywords/parse-tree","display_name":"Parse tree","score":0.5478649735450745},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5198146104812622},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.5192953944206238},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5106812119483948},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49456116557121277},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.47724342346191406},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4319204092025757},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.4102801978588104},{"id":"https://openalex.org/keywords/parsing","display_name":"Parsing","score":0.3660394251346588},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34636616706848145},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28652453422546387},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.10556194186210632},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09276220202445984},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07685118913650513},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06258201599121094}],"concepts":[{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6185356378555298},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5739428997039795},{"id":"https://openalex.org/C2781466058","wikidata":"https://www.wikidata.org/wiki/Q627921","display_name":"Parse tree","level":3,"score":0.5478649735450745},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5198146104812622},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.5192953944206238},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5106812119483948},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49456116557121277},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.47724342346191406},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4319204092025757},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.4102801978588104},{"id":"https://openalex.org/C186644900","wikidata":"https://www.wikidata.org/wiki/Q194152","display_name":"Parsing","level":2,"score":0.3660394251346588},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34636616706848145},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28652453422546387},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.10556194186210632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09276220202445984},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07685118913650513},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06258201599121094},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:9905","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.6","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},{"id":"pmh:oai:arXiv.org:1709.03068","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.03068","pdf_url":"https://arxiv.org/pdf/1709.03068","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":"","raw_type":"text"},{"id":"doi:10.48550/arxiv.1709.03068","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.03068","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.4230/lipics.fsttcs.2018.6","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.fsttcs.2018.6","pdf_url":null,"source":{"id":"https://openalex.org/S7407052059","display_name":"Dagstuhl Research Online Publication Server","issn_l":null,"issn":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":""}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:9905","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.6","pdf_url":null,"source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320322596","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1503731768","https://openalex.org/W1599026900","https://openalex.org/W1984806876","https://openalex.org/W2142326730","https://openalex.org/W2170831059","https://openalex.org/W2490952112","https://openalex.org/W2611754984","https://openalex.org/W2787135910","https://openalex.org/W2949308554"],"related_works":["https://openalex.org/W4244615522","https://openalex.org/W1972256049","https://openalex.org/W2338828339","https://openalex.org/W2049995120","https://openalex.org/W2166677757","https://openalex.org/W2141288413","https://openalex.org/W3123688778","https://openalex.org/W1634973882","https://openalex.org/W2033808215","https://openalex.org/W1994456160"],"abstract_inverted_index":{"We":[0],"study":[1,141],"the":[2,38,103,111,123,167],"class":[3],"of":[4,16,46,57,75,89,102,105,113,143,166],"non-commutative":[5,144],"Unambiguous":[6],"circuits":[7,19,62,80,159],"or":[8],"Unique-Parse-Tree":[9],"(UPT)":[10],"circuits,":[11,51,115],"and":[12,27,30,33,36,108,116,160,172],"a":[13,87,94,163],"related":[14],"model":[15],"Few-Parse-Trees":[17],"(FewPT)":[18],"(which":[20],"were":[21],"recently":[22],"introduced":[23],"by":[24,93],"Lagarde,":[25,31],"Malod":[26],"Perifel":[28],"[LMP16]":[29],"Limaye":[32],"Srinivasan":[34],"[LLS17])":[35],"give":[37],"following":[39],"constructions:":[40],"(1)":[41],"An":[42,53,71],"explicit":[43,54,72],"hitting":[44,55,73],"set":[45,56,74],"quasipolynomial":[47,58],"size":[48,59,77],"for":[49,60,78,157],"UPT":[50,79,114,158],"(2)":[52],"FewPT":[61],"(circuits":[63],"with":[64],"constantly":[65],"many":[66],"parse":[67,83],"tree":[68,84],"shapes),":[69],"(3)":[70],"polynomial":[76],"(of":[81],"known":[82],"shape),":[85],"when":[86],"parameter":[88],"preimage-width":[90],"is":[91,139],"bounded":[92],"constant.":[95],"The":[96,136],"above":[97],"three":[98],"results":[99,104,121,156],"are":[100],"extensions":[101],"[AGKS15],":[106,170],"[GKST15]":[107,171],"[GKS16]":[109],"to":[110,133,140,151],"setting":[112],"hence":[117],"also":[118],"generalize":[119],"their":[120],"in":[122,169],"commutative":[124],"world":[125],"from":[126],"read-once":[127],"oblivious":[128],"algebraic":[129],"branching":[130],"programs":[131],"(ROABPs)":[132],"UPT-set-multilinear":[134],"circuits.":[135],"main":[137],"idea":[138],"shufflings":[142],"polynomials,":[145],"which":[146],"can":[147],"then":[148],"be":[149],"used":[150],"prove":[152],"suitable":[153],"depth":[154],"reduction":[155],"thereby":[161],"allow":[162],"careful":[164],"translation":[165],"ideas":[168],"[GKS16].":[173]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2017-09-25T00:00:00"}