{"id":"https://openalex.org/W3005304592","doi":"https://doi.org/10.1145/3357713.3384263","title":"The program-size complexity of self-assembled paths","display_name":"The program-size complexity of self-assembled paths","publication_year":2020,"publication_date":"2020-06-07","ids":{"openalex":"https://openalex.org/W3005304592","doi":"https://doi.org/10.1145/3357713.3384263","mag":"3005304592"},"language":"en","primary_location":{"id":"doi:10.1145/3357713.3384263","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3357713.3384263","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3357713.3384263","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://dl.acm.org/doi/pdf/10.1145/3357713.3384263","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013696498","display_name":"Pierre-\u00c9tienne Meunier","orcid":null},"institutions":[{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Pierre-\u00c9tienne Meunier","raw_affiliation_strings":["Maynooth University, Ireland","Maynooth University Ireland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Maynooth University, Ireland","institution_ids":["https://openalex.org/I157286207"]},{"raw_affiliation_string":"Maynooth University Ireland#TAB#","institution_ids":["https://openalex.org/I157286207"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047854195","display_name":"Damien Regnault","orcid":"https://orcid.org/0000-0001-9815-5606"},"institutions":[{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I88467170","display_name":"Universit\u00e9 d'\u00c9vry Val-d'Essonne","ror":"https://ror.org/00e96v939","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954","https://openalex.org/I88467170"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Damien Regnault","raw_affiliation_strings":["University of \u00c9vry, France / University of Paris-Saclay, France","University of Evry-Val d'Essonne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of \u00c9vry, France / University of Paris-Saclay, France","institution_ids":["https://openalex.org/I88467170","https://openalex.org/I277688954"]},{"raw_affiliation_string":"University of Evry-Val d'Essonne","institution_ids":["https://openalex.org/I88467170"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029275026","display_name":"Damien Woods","orcid":"https://orcid.org/0000-0002-0638-2690"},"institutions":[{"id":"https://openalex.org/I157286207","display_name":"National University of Ireland, Maynooth","ror":"https://ror.org/048nfjm95","country_code":"IE","type":"education","lineage":["https://openalex.org/I157286207"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Damien Woods","raw_affiliation_strings":["Maynooth University, Ireland","Maynooth University Ireland#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Maynooth University, Ireland","institution_ids":["https://openalex.org/I157286207"]},{"raw_affiliation_string":"Maynooth University Ireland#TAB#","institution_ids":["https://openalex.org/I157286207"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0834,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42765286,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"727","last_page":"737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","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/T12784","display_name":"Modular Robots and Swarm Intelligence","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tile","display_name":"Tile","score":0.7524471282958984},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.5769144296646118},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5709320902824402},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5367938280105591},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.49876976013183594},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.4939785599708557},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.49309608340263367},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.40324485301971436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3923647999763489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3160548210144043},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09838670492172241}],"concepts":[{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.7524471282958984},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5769144296646118},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5709320902824402},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5367938280105591},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.49876976013183594},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.4939785599708557},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.49309608340263367},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.40324485301971436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3923647999763489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3160548210144043},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09838670492172241},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","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},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1145/3357713.3384263","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3357713.3384263","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3357713.3384263","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:mural.maynoothuniversity.ie:15712","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196372","display_name":"MURAL - Maynooth University Research Archive Library (National University of Ireland, Maynooth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157286207","host_organization_name":"National University of Ireland, Maynooth","host_organization_lineage":["https://openalex.org/I157286207"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:arXiv.org:2002.04012","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.04012","pdf_url":"https://arxiv.org/pdf/2002.04012","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":"mag:3005304592","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2002.04012.pdf","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-02866950v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02866950","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"52nd Annual ACM SIGACT Symposium on Theory of Computing (STOC 2020), Jun 2020, Chicago, IL, United States. pp.727--737, &#x27E8;10.1145/3357713.3384263&#x27E9;","raw_type":"Conference papers"},{"id":"doi:10.48550/arxiv.2002.04012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2002.04012","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:10.1145/3357713.3384263","is_oa":true,"landing_page_url":"https://doi.org/10.1145/3357713.3384263","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/3357713.3384263","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7687964855","display_name":null,"funder_award_id":"772766","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3005304592.pdf","grobid_xml":"https://content.openalex.org/works/W3005304592.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1512044279","https://openalex.org/W1543325459","https://openalex.org/W1554356191","https://openalex.org/W1580526823","https://openalex.org/W1607359365","https://openalex.org/W1608283001","https://openalex.org/W1639950410","https://openalex.org/W1722100670","https://openalex.org/W1723666355","https://openalex.org/W1760837217","https://openalex.org/W1790022014","https://openalex.org/W1831806611","https://openalex.org/W1910846469","https://openalex.org/W1948499615","https://openalex.org/W1981863124","https://openalex.org/W1982939827","https://openalex.org/W1983241546","https://openalex.org/W1990819744","https://openalex.org/W2000567812","https://openalex.org/W2019553804","https://openalex.org/W2024827079","https://openalex.org/W2041882287","https://openalex.org/W2044709436","https://openalex.org/W2062802768","https://openalex.org/W2063465004","https://openalex.org/W2064143748","https://openalex.org/W2070322565","https://openalex.org/W2070783600","https://openalex.org/W2079425200","https://openalex.org/W2086507196","https://openalex.org/W2112626116","https://openalex.org/W2135520597","https://openalex.org/W2214429455","https://openalex.org/W2302577799","https://openalex.org/W2565088752","https://openalex.org/W2585365870","https://openalex.org/W2596304771","https://openalex.org/W2620826411","https://openalex.org/W2784847360","https://openalex.org/W2924487690","https://openalex.org/W2963600281","https://openalex.org/W2963927118","https://openalex.org/W2966809659"],"related_works":["https://openalex.org/W2784847360","https://openalex.org/W421751177","https://openalex.org/W3003022809","https://openalex.org/W2615868730","https://openalex.org/W2972345041","https://openalex.org/W1540568511","https://openalex.org/W2405609219","https://openalex.org/W2951050348","https://openalex.org/W1640823551","https://openalex.org/W1603704056","https://openalex.org/W2265857168","https://openalex.org/W2950067352","https://openalex.org/W3013169761","https://openalex.org/W2301473048","https://openalex.org/W3036464028","https://openalex.org/W1995059218","https://openalex.org/W2199664063","https://openalex.org/W2151741604","https://openalex.org/W2056218894","https://openalex.org/W1586552034"],"abstract_inverted_index":{"We":[0,172],"prove":[1,167],"a":[2,12,195],"Pumping":[3],"Lemma":[4],"for":[5,85,116,155,210],"the":[6,16,22,25,38,55,149,229,232,237,240],"noncooperative":[7,123,177],"abstract":[8,44,57],"Tile":[9,58],"Assembly":[10,59],"Model,":[11,60],"model":[13,127],"central":[14],"to":[15,49,64,148,157,181],"theory":[17,28],"of":[18,24,40,70,79,90,102,108,162,203,222,231,239,247],"algorithmic":[19,86,205],"self-assembly":[20,109],"since":[21],"beginning":[23],"field.":[26],"This":[27,76,145],"suggests,":[29],"and":[30,105,213,216,234],"our":[31],"result":[32,208],"proves,":[33],"that":[34,151,174,179],"small":[35],"differences":[36],"in":[37],"nature":[39],"adhesive":[41],"bindings":[42,114],"between":[43],"square":[45,61],"molecules":[46],"gives":[47,217],"rise":[48],"vastly":[50],"different":[51],"expressive":[52],"capabilities.":[53],"In":[54],"cooperative":[56,113],"tiles":[62,135,248],"attach":[63],"each":[65],"other":[66],"using":[67,93],"multi-sided":[68],"cooperation":[69],"one,":[71],"two":[72],"or":[73,199,251],"more":[74],"sides.":[75],"precise":[77],"control":[78,130],"tile":[80,96],"binding":[81,133],"is":[82,153,228,236,249],"directly":[83],"exploited":[84],"tasks":[87],"including":[88],"growth":[89,161],"specified":[91],"shapes":[92],"very":[94],"few":[95],"types,":[97],"as":[98,100],"well":[99],"simulation":[101],"Turing":[103],"machines":[104],"even":[106],"self-simulation":[107],"systems.":[110],"But":[111],"are":[112],"required":[115],"these":[117],"computational":[118],"tasks?":[119],"The":[120],"definitionally":[121],"simpler":[122],"(or":[124],"Temperature":[125],"1)":[126],"has":[128,146],"poor":[129],"over":[131],"local":[132],"events:":[134],"stick":[136],"if":[137],"they":[138],"bind":[139],"on":[140],"at":[141],"least":[142],"one":[143],"side.":[144],"led":[147],"conjecture":[150],"it":[152,156],"impossible":[154],"exhibit":[158],"precisely":[159],"controlled":[160],"computationally-defined":[163],"shapes.":[164],"Here,":[165],"we":[166],"such":[168],"an":[169,218],"impossibility":[170],"result.":[171],"show":[173],"any":[175,245],"planar":[176],"system":[178],"attempts":[180],"grow":[182,189],"large":[183],"algorithmically-controlled":[184],"tile-efficient":[185],"assemblies":[186],"must":[187],"also":[188],"infinite":[190],"non-algorithmic":[191],"(pumped)":[192],"structures":[193],"with":[194],"simple":[196],"closed-form":[197],"description,":[198],"else":[200],"suffer":[201],"blocking":[202],"intended":[204],"structures.":[206],"Our":[207],"holds":[209],"both":[211],"directed":[212],"nondirected":[214],"systems,":[215],"explicit":[219],"upper":[220],"bound":[221],"(8|T|)4|T|+1(5|\u03c3|":[223],"+":[224],"6),":[225],"where":[226],"|T|":[227],"size":[230,238],"tileset":[233],"|\u03c3|":[235],"seed":[241],"assembly,":[242],"beyond":[243],"which":[244],"path":[246],"pumpable":[250],"blockable.":[252]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
