{"id":"https://openalex.org/W7081569447","doi":"https://doi.org/10.48550/arxiv.2509.09657","title":"Uniformity within Parameterized Circuit Classes","display_name":"Uniformity within Parameterized Circuit Classes","publication_year":2025,"publication_date":"2025-09-11","ids":{"openalex":"https://openalex.org/W7081569447","doi":"https://doi.org/10.48550/arxiv.2509.09657"},"language":"en","primary_location":{"id":"doi:10.48550/arxiv.2509.09657","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.09657","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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2509.09657","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Hegeman, Steef","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hegeman, Steef","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Martens, Jan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martens, Jan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Laarman, Alfons","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laarman, Alfons","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":true,"primary_topic":{"id":"https://openalex.org/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.7053999900817871,"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/T12157","display_name":"Geochemistry and Geologic Mapping","score":0.7053999900817871,"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/T13067","display_name":"Geological Modeling and Analysis","score":0.02630000002682209,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14311","display_name":"Electrical and Electromagnetic Research","score":0.016100000590085983,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.9581000208854675},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.582099974155426},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.48249998688697815},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.3982999920845032},{"id":"https://openalex.org/keywords/network-analysis","display_name":"Network analysis","score":0.38659998774528503},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.3725000023841858},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.36970001459121704}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.9581000208854675},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.582099974155426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5047000050544739},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.48249998688697815},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47049999237060547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4133000075817108},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3982999920845032},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.38659998774528503},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.36970001459121704},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.34310001134872437},{"id":"https://openalex.org/C23572009","wikidata":"https://www.wikidata.org/wiki/Q964981","display_name":"Equivalent circuit","level":3,"score":0.32659998536109924},{"id":"https://openalex.org/C113089479","wikidata":"https://www.wikidata.org/wiki/Q210729","display_name":"Electrical element","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.31470000743865967},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C94992772","wikidata":"https://www.wikidata.org/wiki/Q6667469","display_name":"Circuit minimization for Boolean functions","level":4,"score":0.3034999966621399},{"id":"https://openalex.org/C188058453","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Discrete circuit","level":4,"score":0.27160000801086426},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.26840001344680786},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2590999901294708},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25679999589920044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2509.09657","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.09657","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"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2509.09657","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.09657","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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,77],"study":[1],"uniformity":[2,69,110,121],"conditions":[3,10,70],"for":[4,55,60,111],"parameterized":[5,65,80,113],"Boolean":[6],"circuit":[7,19,34,66,114],"families.":[8],"Uniformity":[9],"require":[11],"that":[12,89],"the":[13,56,123],"infinitely":[14],"many":[15],"circuits":[16],"in":[17,22,64,92,122],"a":[18,105],"family":[20],"are":[21],"some":[23],"sense":[24],"easy":[25],"to":[26,43,108],"construct":[27],"from":[28],"one":[29],"shared":[30],"description.":[31],"For":[32],"shallow":[33,112],"families,":[35],"logtime-uniformity":[36],"is":[37,49],"often":[38,50],"desired":[39],"but":[40],"quite":[41],"technical":[42],"prove.":[44],"Despite":[45],"that,":[46],"proving":[47],"it":[48],"left":[51],"as":[52],"an":[53],"exercise":[54],"reader":[57],"--":[58],"even":[59],"recently":[61],"introduced":[62],"classes":[63,95],"complexity,":[67],"where":[68],"have":[71],"not":[72],"yet":[73],"been":[74],"explicitly":[75],"studied.":[76],"formally":[78],"define":[79],"versions":[81],"of":[82,120],"linear-uniformity,":[83],"logtime-uniformity,":[84],"and":[85,87,100,116],"FO-uniformity,":[86],"prove":[88],"these":[90],"result":[91],"equivalent":[93],"complexity":[94],"when":[96],"imposed":[97],"on":[98],"$\\text{para-}\\textsf{AC}^0$":[99],"$\\text{para-}\\textsf{AC}^{0\\uparrow}$.":[101],"Overall,":[102],"we":[103],"provide":[104],"convenient":[106],"way":[107],"verify":[109],"classes,":[115],"thereby":[117],"substantiate":[118],"claims":[119],"literature.":[124]},"counts_by_year":[],"updated_date":"2025-11-06T06:51:31.235846","created_date":"2025-10-10T00:00:00"}