{"id":"https://openalex.org/W2978214882","doi":"https://doi.org/10.1007/s00453-023-01114-2","title":"Parameterised Counting in Logspace","display_name":"Parameterised Counting in Logspace","publication_year":2023,"publication_date":"2023-04-21","ids":{"openalex":"https://openalex.org/W2978214882","doi":"https://doi.org/10.1007/s00453-023-01114-2","mag":"2978214882"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-023-01114-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-023-01114-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01114-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01114-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074189902","display_name":"Anselm Haak","orcid":"https://orcid.org/0000-0003-1031-5922"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Anselm Haak","raw_affiliation_strings":["Theoretical Computer Science Group, Goethe-Universit\u00e4t Frankfurt, Robert-Mayer-Stra\u00dfe 11-15, 60325, Frankfurt, Germany"],"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science Group, Goethe-Universit\u00e4t Frankfurt, Robert-Mayer-Stra\u00dfe 11-15, 60325, Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025571978","display_name":"Arne Meier","orcid":"https://orcid.org/0000-0002-8061-5376"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Arne Meier","raw_affiliation_strings":["Institut f\u00fcr Theoretische Informatik, Leibniz Universit\u00e4t Hannover, Appelstrasse 9A, 30167, Hannover, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Theoretische Informatik, Leibniz Universit\u00e4t Hannover, Appelstrasse 9A, 30167, Hannover, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043581743","display_name":"Om Prakash","orcid":"https://orcid.org/0000-0003-0482-072X"},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Om Prakash","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT Madras, BSB 354, Chennai, 600 036, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT Madras, BSB 354, Chennai, 600 036, India","institution_ids":["https://openalex.org/I24676775"]}]},{"author_position":"last","author":{"id":null,"display_name":"B. V. Raghavendra Rao","orcid":null},"institutions":[{"id":"https://openalex.org/I24676775","display_name":"Indian Institute of Technology Madras","ror":"https://ror.org/03v0r5n49","country_code":"IN","type":"facility","lineage":["https://openalex.org/I24676775"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"B. V. Raghavendra Rao","raw_affiliation_strings":["Department of Computer Science and Engineering, IIT Madras, BSB 354, Chennai, 600 036, India"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, IIT Madras, BSB 354, Chennai, 600 036, India","institution_ids":["https://openalex.org/I24676775"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074189902"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.5899,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.68399044,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"85","issue":"10","first_page":"2923","last_page":"2961"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.3046000003814697,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.3046000003814697,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.2513999938964844,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.24050000309944153,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.7103043794631958},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6680381894111633},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5909422039985657},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4921032786369324},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.4900859594345093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.48945513367652893},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.4802544414997101},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.4708765745162964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.465774267911911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4598918557167053},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43835264444351196},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4383390545845032},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4145740866661072},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3492888808250427},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2216205596923828}],"concepts":[{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.7103043794631958},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6680381894111633},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5909422039985657},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4921032786369324},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.4900859594345093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.48945513367652893},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.4802544414997101},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.4708765745162964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.465774267911911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4598918557167053},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43835264444351196},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4383390545845032},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4145740866661072},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3492888808250427},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2216205596923828},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","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}],"mesh":[],"locations_count":10,"locations":[{"id":"doi:10.1007/s00453-023-01114-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-023-01114-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01114-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:drops-oai.dagstuhl.de:13690","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.45","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:1904.12156","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1904.12156","pdf_url":"https://arxiv.org/pdf/1904.12156","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":null,"raw_type":"text"},{"id":"pmh:oai:arXiv.org:2010.13170","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2010.13170","pdf_url":"https://arxiv.org/pdf/2010.13170","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":null,"raw_type":"text"},{"id":"pmh:oai:www.repo.uni-hannover.de:123456789/15001","is_oa":true,"landing_page_url":"https://www.repo.uni-hannover.de/handle/123456789/15001","pdf_url":"https://repo.uni-hannover.de/bitstreams/20696b90-30e5-480a-9626-ce53599815a2/download","source":{"id":"https://openalex.org/S4306401575","display_name":"Institutional Repository of Leibniz Universit\u00e4t Hannover (Leibniz Universit\u00e4t Hannover)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114112103","host_organization_name":"Leibniz University Hannover","host_organization_lineage":["https://openalex.org/I114112103"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica 85 (2023)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:drops-oai.dagstuhl.de:13685","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.40","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"InProceedings"},{"id":"doi:10.48550/arxiv.1904.12156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1904.12156","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-journal"},{"id":"doi:10.15488/14882","is_oa":true,"landing_page_url":"https://doi.org/10.15488/14882","pdf_url":null,"source":{"id":"https://openalex.org/S7407052956","display_name":"Leibniz Universit\u00e4t Hannover","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":"article-journal"},{"id":"doi:10.4230/lipics.stacs.2021.40","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.stacs.2021.40","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":""},{"id":"doi:10.4230/lipics.stacs.2021.45","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.stacs.2021.45","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":"doi:10.1007/s00453-023-01114-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-023-01114-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-023-01114-2.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"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":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G938901808","display_name":null,"funder_award_id":"ME4279/1-2","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"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/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322379","display_name":"Gottfried Wilhelm Leibniz Universit\u00e4t Hannover","ror":"https://ror.org/0304hq317"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2978214882.pdf"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W36639738","https://openalex.org/W154868527","https://openalex.org/W1489417824","https://openalex.org/W1490189322","https://openalex.org/W1508570999","https://openalex.org/W1516803018","https://openalex.org/W1527197079","https://openalex.org/W1554948556","https://openalex.org/W1570425181","https://openalex.org/W1585305311","https://openalex.org/W1592302951","https://openalex.org/W1872333393","https://openalex.org/W1978001037","https://openalex.org/W1987889357","https://openalex.org/W1988772559","https://openalex.org/W1994584977","https://openalex.org/W2006912660","https://openalex.org/W2033042995","https://openalex.org/W2040145343","https://openalex.org/W2044535619","https://openalex.org/W2046652577","https://openalex.org/W2049559029","https://openalex.org/W2080370600","https://openalex.org/W2083553352","https://openalex.org/W2088101961","https://openalex.org/W2102039892","https://openalex.org/W2106472514","https://openalex.org/W2106991838","https://openalex.org/W2111829945","https://openalex.org/W2123466414","https://openalex.org/W2128626931","https://openalex.org/W2137407595","https://openalex.org/W2137874581","https://openalex.org/W2148322175","https://openalex.org/W2171197316","https://openalex.org/W2178086598","https://openalex.org/W2221820168","https://openalex.org/W2236332462","https://openalex.org/W2260560831","https://openalex.org/W2296148711","https://openalex.org/W2397172610","https://openalex.org/W2464394875","https://openalex.org/W2477674116","https://openalex.org/W2537667430","https://openalex.org/W2553008661","https://openalex.org/W2563912921","https://openalex.org/W2610844084","https://openalex.org/W2789507435","https://openalex.org/W2798555189","https://openalex.org/W2913688336","https://openalex.org/W2914509905","https://openalex.org/W2956649389","https://openalex.org/W2963279056","https://openalex.org/W2963562591","https://openalex.org/W2963579754","https://openalex.org/W3120183386","https://openalex.org/W3210858999","https://openalex.org/W4212838967","https://openalex.org/W4212998659","https://openalex.org/W4230626603","https://openalex.org/W4237721941","https://openalex.org/W4283816481","https://openalex.org/W4292230561","https://openalex.org/W4298227433"],"related_works":["https://openalex.org/W3138646347","https://openalex.org/W2171197316","https://openalex.org/W1687766689","https://openalex.org/W2007706420","https://openalex.org/W2002941015","https://openalex.org/W2952440918","https://openalex.org/W2059824826","https://openalex.org/W2018354266","https://openalex.org/W3175190083","https://openalex.org/W206840222","https://openalex.org/W47988892","https://openalex.org/W1580836907","https://openalex.org/W2151310684","https://openalex.org/W2080097400","https://openalex.org/W1582402643","https://openalex.org/W2059442203","https://openalex.org/W2056870994","https://openalex.org/W2259552592","https://openalex.org/W1563646575","https://openalex.org/W2962798967"],"abstract_inverted_index":{"Abstract":[0],"Logarithmic":[1],"space-bounded":[2,21,76,111],"complexity":[3,30,58,134,153,241],"classes":[4,31,135,360],"such":[5,44],"as":[6,45,264],"$$\\textbf{L}":[7,207],"$$":[8,13,128,170,208,256,273,307,319],"<mml:math":[9,14,124,129,166,171,184,189,209,257,274,308,320],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>L</mml:mi></mml:math>":[10,210],"and":[11,49,68,88,117,126,142,168,175,186,201,232,260,365,367,397],"$$\\textbf{NL}":[12],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>NL</mml:mi></mml:math>":[15],"play":[16],"a":[17,70,99,243,390],"central":[18],"role":[19],"in":[20,52,81,105,225,270,326],"computation.":[22],"The":[23],"study":[24,72,345],"of":[25,28,41,73,154,162,197,223,242,246,267,282,294,304,329,346,349,385],"counting":[26,50,104,195,222,227,233,285,353],"versions":[27,196],"these":[29,147,295,350],"have":[32],"lead":[33],"to":[34,204,332,381],"several":[35,214,394],"interesting":[36,291],"insights":[37],"into":[38],"the":[39,47,82,109,121,151,160,163,205,219,240,247,265,280,283,302,327,344,383],"structure":[40],"computational":[42],"problems":[43,156,217,278,396],"computing":[46],"determinant":[48,248],"paths":[51,224],"directed":[53],"acyclic":[54],"graphs.":[55,158],"Though":[56],"parameterised":[57,74,103,110,132,152,244,311,341,351,374],"theory":[59],"was":[60,78],"initiated":[61],"roughly":[62],"three":[63],"decades":[64],"ago":[65],"by":[66,85,108,114,136,173,388],"Downey":[67],"Fellows,":[69],"satisfactory":[71],"logarithmic":[75],"computation":[77],"developed":[79,113],"only":[80],"last":[83],"decade":[84],"Elberfeld,":[86,115],"Stockhusen":[87,116,174],"Tantau":[89],"(IPEC":[90],"2013,":[91],"Algorithmica":[92],"2015).":[93],"In":[94,159,323],"this":[95,386],"paper,":[96],"we":[97,177,193,237,299,355,379],"introduce":[98,178],"new":[100],"framework":[101],"for":[102,131,218,230,250,399],"logspace,":[106],"inspired":[107],"models":[112,229],"Tantau.":[118],"They":[119],"defined":[120],"operators":[122,164,200],"$$\\textbf{para}_{\\textbf{W}}$$":[123,165],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>para</mml:mi><mml:mi>W</mml:mi></mml:msub></mml:math>":[125,167],"$$\\textbf{para}_\\beta":[127,169],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>para</mml:mi><mml:mi>\u03b2</mml:mi></mml:msub></mml:math>":[130,172],"space":[133],"allowing":[137],"bounded":[138],"nondeterminism":[139,339],"with":[140,316,337],"multiple-read":[141],"read-once":[143,330],"access,":[144],"respectively.":[145],"Using":[146],"operators,":[148],"they":[149],"characterised":[150],"natural":[155,215],"on":[157,181],"spirit":[161],"Tantau,":[176],"variants":[179],"based":[180],"tail-nondeterminism,":[182],"$$\\textbf{para}_{{\\textbf{W}}[1]}$$":[183],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>para</mml:mi><mml:mrow><mml:mi>W</mml:mi><mml:mo>[</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:msub></mml:math>":[185],"$$\\textbf{para}_{\\beta":[187],"{\\textbf{tail}}}$$":[188],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>para</mml:mi><mml:mrow><mml:mi>\u03b2</mml:mi><mml:mi>tail</mml:mi></mml:mrow></mml:msub></mml:math>":[190],".":[191,211,276,322],"Then,":[192],"consider":[194],"all":[198,358],"four":[199],"apply":[202],"them":[203],"class":[206],"We":[212],"obtain":[213],"complete":[216],"resulting":[220],"classes:":[221],"digraphs,":[226],"first-order":[228],"formulas,":[231],"graph":[234],"homomorphisms.":[235],"Furthermore,":[236],"show":[238,300,356],"that":[239,301,357],"variant":[245],"function":[249],"(0,":[251],"1)-matrices":[252],"is":[253],"$$\\#\\textbf{para}_{\\beta":[254,271,305],"{\\textbf{tail}}}\\textbf{L}":[255,272,306],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mo>#</mml:mo><mml:msub><mml:mi>para</mml:mi><mml:mrow><mml:mi>\u03b2</mml:mi><mml:mi>tail</mml:mi></mml:mrow></mml:msub><mml:mi>L</mml:mi></mml:mrow></mml:math>":[258,275,309],"-hard":[259],"can":[261],"be":[262],"written":[263],"difference":[266],"two":[268],"functions":[269],"These":[277],"exhibit":[279],"richness":[281],"introduced":[284,359],"classes.":[286,296],"Our":[287],"results":[288],"further":[289,400],"indicate":[290],"structural":[292],"characteristics":[293],"For":[297],"example,":[298],"closure":[303,347],"under":[310,363,373],"logspace":[312,352,375],"parsimonious":[313,376],"reductions":[314],"coincides":[315,336],"$$\\#\\textbf{para}_\\beta":[317],"\\textbf{L}":[318],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mo>#</mml:mo><mml:msub><mml:mi>para</mml:mi><mml:mi>\u03b2</mml:mi></mml:msub><mml:mi>L</mml:mi></mml:mrow></mml:math>":[321],"other":[324],"words,":[325],"setting":[328],"access":[331],"nondeterministic":[333],"bits,":[334],"tail-nondeterminism":[335,370],"unbounded":[338],"modulo":[340],"reductions.":[342,377],"Initiating":[343],"properties":[348],"classes,":[354],"are":[361,371],"closed":[362,372],"addition":[364],"multiplication,":[366],"those":[368],"without":[369],"Finally,":[378],"want":[380],"emphasise":[382],"significance":[384],"topic":[387],"providing":[389],"promising":[391],"outlook":[392],"highlighting":[393],"open":[395],"directions":[398],"research.":[401]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-10-10T00:00:00"}