{"id":"https://openalex.org/W7225586152","doi":"https://doi.org/10.5281/zenodo.24057439","title":"Soluble State Tracking in Materialized Fixed-Point GDN+","display_name":"Soluble State Tracking in Materialized Fixed-Point GDN+","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225586152","doi":"https://doi.org/10.5281/zenodo.24057439"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24057439","doi":"https://doi.org/10.5281/zenodo.24057439","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24057439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24057439","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161274316","display_name":"Tarang Khanna","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Khanna, Tarang","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161274316"],"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":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9897000193595886,"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/T11567","display_name":"semigroups and automata theory","score":0.9897000193595886,"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/T12162","display_name":"Cellular Automata and Applications","score":0.002300000051036477,"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/T10320","display_name":"Neural Networks and Applications","score":0.0010000000474974513,"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/cyclic-groups","display_name":"cyclic groups","score":0.6330000162124634},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.6140000224113464}],"concepts":[{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.6639000177383423},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.6471999883651733},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.63919997215271},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5877000093460083},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.4997999966144562},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49070000648498535},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45969998836517334},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45890000462532043},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45809999108314514},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.44940000772476196},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4348999857902527},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.4162999987602234},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4131999909877777},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4090000092983246},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.37599998712539673},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35019999742507935},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3402999937534332},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.31850001215934753},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.3089999854564667},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C38677869","wikidata":"https://www.wikidata.org/wiki/Q724168","display_name":"Petri net","level":2,"score":0.30399999022483826},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.2906000018119812},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C159333733","wikidata":"https://www.wikidata.org/wiki/Q7051809","display_name":"Normalization property","level":2,"score":0.2773999869823456},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.27480000257492065},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.2578999996185303},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.25189998745918274},{"id":"https://openalex.org/C9555016","wikidata":"https://www.wikidata.org/wiki/Q828111","display_name":"Zero divisor","level":2,"score":0.25119999051094055},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25110000371932983}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24057439","doi":"https://doi.org/10.5281/zenodo.24057439","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24057439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5281/zenodo.24057440","doi":"https://doi.org/10.5281/zenodo.24057440","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24057440","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.5281/zenodo.24057439","doi":"https://doi.org/10.5281/zenodo.24057439","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24057439","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1490839772","https://openalex.org/W1970452008","https://openalex.org/W2499062423","https://openalex.org/W1996721275","https://openalex.org/W174309257","https://openalex.org/W7096921744","https://openalex.org/W1969832165","https://openalex.org/W7036878123","https://openalex.org/W7098951550","https://openalex.org/W2954602097"],"abstract_inverted_index":{"Every":[0],"finite":[1,90],"soluble":[2,57],"monoid":[3],"admits":[4],"a":[5,96,100],"fixed-width,":[6],"fixed-depth":[7],"GDN\u207a":[8],"network":[9],"that":[10,78],"computes":[11],"its":[12],"nonempty":[13],"prefix":[14,106],"products":[15,67],"in":[16,59],"the":[17,104,124],"materialized":[18],"fixed-point":[19],"model":[20],"defined":[21],"here,":[22],"with":[23],"constant":[24],"gates":[25],"\u03b1":[26],"=":[27,29],"\u03b2":[28],"1,":[30],"zero":[31],"initial":[32],"memory,":[33],"and":[34,44,54,81,84,116],"either":[35],"of":[36],"two":[37],"specified":[38],"centered":[39],"normalizations.":[40],"StateBench":[41],"establishes":[42],"aperiodic":[43],"rounded-parity":[45],"lower":[46],"bounds;":[47],"our":[48],"construction":[49],"supplies":[50,103],"all":[51],"cyclic":[52],"factors":[53],"their":[55],"full-network":[56],"composition":[58],"this":[60],"explicit":[61],"operational":[62],"model.":[63],"Individually":[64],"rounded":[65],"matrix":[66],"implement":[68],"bounded":[69],"modular":[70],"counters.":[71],"Cyclically":[72],"shifted":[73],"copies":[74],"expose":[75],"constant-norm":[76],"codes":[77],"survive":[79],"normalization":[80],"residual":[82],"addition,":[83],"bias-free":[85],"ReLU":[86],"selectors":[87],"return":[88],"reusable":[89],"labels.":[91],"A":[92],"first-position":[93],"marker":[94],"replaces":[95],"beginning-of-sequence":[97],"token,":[98],"while":[99],"parity-driven":[101],"buffer":[102],"exclusive":[105],"required":[107],"by":[108],"wreath":[109],"composition.":[110],"Exact":[111],"certificates":[112],"exhaust":[113],"complete":[114],"modulo-three":[115],"\u2124\u2083":[117],"\u2240":[118],"U\u2082":[119],"networks":[120],"under":[121],"both":[122],"normalizations;":[123],"universal":[125],"claim":[126],"follows":[127],"from":[128],"an":[129],"algebraic":[130],"induction.":[131]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}