[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81761-en":3,"doc-seo-81761-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81761,4398048949847,"Eliana","https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267",8,"Research & Report","Feasibilism, Explication, and the Cobham-Edmonds Thesis","The paper contrasts the Church–Turing thesis with the Cobham–Edmonds thesis, arguing that effective calculability corresponds to decidable sets recognized by a Turing machine, whereas feasible computation corresponds to the complexity class P, decidable by polynomial-time bounded Turing machines. It notes that the Church–Turing thesis has received extensive scrutiny, while Cobham–Edmonds has not. It develops analogous supporting arguments and analyzes feasibility through notions like predicativity, bounded constructivity, and physical constraints, addressing obstacles to making the explicatum precise.","arXiv :2607 .003 15v 1 [ cs .CC] 1 Jul 2026  \nFeasibilism, Explication, and the Cobham-Edmonds Thesis  \nAbrahim Ladha∗ Yiran Luo† Alan Tian‡  \nJuly 2, 2026  \nAbstract  \nWhile the Church-Turing thesis asserts that effective calculability explicates to sets decidable by a Turing machine, the Cobham-Edmonds thesis asserts that feasible computation explicates to the complexity class P, those decidable by a polynomial-time bounded Turing machine. The Church-Turing thesis has been placed under rigorous scrutiny and has several convincing arguments in its favor, but the Cobham-Edmonds thesis has not undergone a similar examination. Many of the arguments in its favor simply suggest that P is a useful assumption, rather than a necessary target. This paper presents analogous arguments in favor of the Cobham-Edmonds thesis.  \nContents  \n1 Background 2  \n1.1 Historical and Philosophical Remarks .......................... 3  \n1.2 Explication and Feasibilism ................................ 4  \n1.3 Computational Complexity ................................ 5  \n1.4 Cobham and Edmonds ................................... 5  \n2 P as a Plausible Hypothesis 6  \n2.1 Uniformity ......................................... 6  \n2.2 Stratospheric but within P ................................. 7  \n2.3 Closure ........................................... 8  \n2.4 The Extended Church Turing Thesis ........................... 8  \n3 Feasibility as Predicativity and Constructivity 9  \n3.1 Feasibility as Predicativity ................................. 10  \n3.1.1 Predicativity and Predicativism .......................... 10  \n3.1.2 Recursion-theoretical context ........................... 11  \n3.1.3 Predicativity in Recursion Theory ........................ 12  \n3.2 Feasibility as Bounded Constructivity .......................... 13  \n3.2.1 Computation and Reasoning ........................... 14  \n∗ Georgia Institute of Technology. Email: [abrahimladha@gatech.edu](abrahimladha@gatech.edu)[ ](abrahimladha@gatech.edu)†Georgia Institute of Technology. Email: [yluo432@gatech.edu](yluo432@gatech.edu)[ ](yluo432@gatech.edu)‡Carnegie Mellon University. Email: [alantian@andrew.cmu.edu](alantian@andrew.cmu.edu)  \n3.2.2 Reasoning in Bounded Arithmetic ........................ 14  \n3.2.3 Later Development and Connection to Complexity Theory ........... 16  \n3.2.4 Li: Feasible Mathematics and PV ......................... 17  \n4 Feasibility as Physical Limitations 18  \n4.1 Grounding Explication in Physics ............................. 18  \n4.2 Discrete Physical Systems and Computability ...................... 19  \n4.3 Complexity of Analog Physical Computers ........................ 20  \n5 Proving the Cobham-Edmonds thesis 21  \n5.1 Turing’s Thesis and Feasibilism .............................. 21  \n5.2 Gandy’s Thesis and Feasibilism .............................. 23  \n5.3 Kripke’s Thesis and Feasibilism .............................. 24  \n6 Failing to make the Explicatum Precise 27  \n6.1 Why is Complexity Theory so Hard? ........................... 27  \n6.2 Feasibility and Randomness ................................ 28  \n6.2.1 Randomized Computation ............................. 28  \n6.2.2 The Explication of Feasible Randomized Computation ............. 29  \n6.3 The Extended Church-Turing Thesis ........................... 31  \n6.3.1 Quantum Computation .............................. 31  \n7 Concluding Remarks 32  \n7.1 Open Problems ....................................... 32  \n7.2 Future Applications of this Analysis ........................... 34  \n1 Background  \nStructural complexity classes are bounded versions of classes in computability theory. While computable languages are those which have a Turing machine which halts on all inputs eventually, languages in P are those which have a Turing machine which halts within a number of steps bounded by a polynomial in the size of the input. While the computably enumerable languages are those which can be witnessed, NP is the class ","cbCaiexn1lKDaqYd","https://ap.wps.com/l/cbCaiexn1lKDaqYd","pdf",556931,3,1,40,"English","en",105,"# Background\n## Historical and Philosophical Remarks\n## Explication and Feasibilism\n## Computational Complexity\n## Cobham and Edmonds\n# P as a Plausible Hypothesis\n## Uniformity\n## Stratospheric but within P\n## Closure\n## The Extended Church Turing Thesis\n# Feasibility as Predicativity and Constructivity\n## Feasibility as Predicativity\n## Feasibility as Bounded Constructivity","[{\"question\":\"What do the Church–Turing and Cobham–Edmonds theses each claim about computation?\",\"answer\":\"The Church–Turing thesis links effective calculability to what is decidable by a Turing machine. The Cobham–Edmonds thesis links feasible computation to what is decidable within polynomial time by a Turing machine, i.e., the class P.\"},{\"question\":\"Why does the paper say the Cobham–Edmonds thesis needs further examination?\",\"answer\":\"It argues that many existing arguments merely present P as a convenient assumption rather than establishing P as the necessary target. The paper proposes analogous arguments directly supporting the Cobham–Edmonds thesis.\"},{\"question\":\"How does the paper develop “feasibility” beyond a purely abstract notion?\",\"answer\":\"It analyzes feasibility through predicativity and bounded constructivity, and also considers feasibility grounded in physical limitations, including the role of discrete physical systems and the complexity of analog physical computers.\"}]",1784175885,101,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"feasibilism-explication-and-the-cobham-edmonds-thesis","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/feasibilism-explication-and-the-cobham-edmonds-thesis/81761/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What do the Church–Turing and Cobham–Edmonds theses each claim about computation?","Question",{"text":75,"@type":76},"The Church–Turing thesis links effective calculability to what is decidable by a Turing machine. The Cobham–Edmonds thesis links feasible computation to what is decidable within polynomial time by a Turing machine, i.e., the class P.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why does the paper say the Cobham–Edmonds thesis needs further examination?",{"text":80,"@type":76},"It argues that many existing arguments merely present P as a convenient assumption rather than establishing P as the necessary target. The paper proposes analogous arguments directly supporting the Cobham–Edmonds thesis.",{"name":82,"@type":73,"acceptedAnswer":83},"How does the paper develop “feasibility” beyond a purely abstract notion?",{"text":84,"@type":76},"It analyzes feasibility through predicativity and bounded constructivity, and also considers feasibility grounded in physical limitations, including the role of discrete physical systems and the complexity of analog physical computers.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":22,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]