{"title":"光线追踪-计算不可计算的?","authors":"Ed Blakey","doi":"10.4204/EPTCS.143.3","DOIUrl":null,"url":null,"abstract":"We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical, error-prone (especially analogue rather than digital) computational systems. We take as a case study the ray-tracing problem, a Turing-machine-incomputable problem that can, in apparent violation of the Church-Turing thesis, nonetheless be said to be solved by certain optical computers; however, we apply the framework of complexity theory so as to formalize the intuition that the purported super-Turing power of these computers in fact vanishes once precision is properly considered.","PeriodicalId":88470,"journal":{"name":"Dialogues in cardiovascular medicine : DCM","volume":"1 1","pages":"32-40"},"PeriodicalIF":0.0000,"publicationDate":"2014-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Ray tracing - computing the incomputable?\",\"authors\":\"Ed Blakey\",\"doi\":\"10.4204/EPTCS.143.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical, error-prone (especially analogue rather than digital) computational systems. We take as a case study the ray-tracing problem, a Turing-machine-incomputable problem that can, in apparent violation of the Church-Turing thesis, nonetheless be said to be solved by certain optical computers; however, we apply the framework of complexity theory so as to formalize the intuition that the purported super-Turing power of these computers in fact vanishes once precision is properly considered.\",\"PeriodicalId\":88470,\"journal\":{\"name\":\"Dialogues in cardiovascular medicine : DCM\",\"volume\":\"1 1\",\"pages\":\"32-40\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-03-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dialogues in cardiovascular medicine : DCM\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4204/EPTCS.143.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dialogues in cardiovascular medicine : DCM","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4204/EPTCS.143.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We recall from previous work a model-independent framework of computational complexity theory. Notably for the present paper, the framework allows formalization of the issues of precision that present themselves when one considers physical, error-prone (especially analogue rather than digital) computational systems. We take as a case study the ray-tracing problem, a Turing-machine-incomputable problem that can, in apparent violation of the Church-Turing thesis, nonetheless be said to be solved by certain optical computers; however, we apply the framework of complexity theory so as to formalize the intuition that the purported super-Turing power of these computers in fact vanishes once precision is properly considered.