{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T20:00:09Z","timestamp":1762459209447},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p> We argue that dynamical systems involving discrete and continuous data can be modelled by Turing machines with oracles that are physical processes. Using the theory introduced in Beggs et al. [2,3], we consider the scope and limits of polynomial time computations by such systems. We propose a general polynomial time Church-Turing Thesis for feasible computations by analogue-digital systems, having the non-uniform complexity class BPP\/\/log* as theoretical upper bound. We show why BPP\/\/log* should be replace P\/poly, which was proposed by Siegelmann for neural nets [23,24]. Then we examine whether other sources of hypercomputation can be found in analogue-digital systems besides the oracle itself. We prove that the higher polytime limit P\/poly can be attained via non-computable analogue-digital interface protocols. <\/jats:p>","DOI":"10.1142\/s0129054114400012","type":"journal-article","created":{"date-parts":[[2014,8,8]],"date-time":"2014-08-08T04:18:49Z","timestamp":1407471529000},"page":"373-389","source":"Crossref","is-referenced-by-count":7,"title":["AN ANALOGUE-DIGITAL CHURCH-TURING THESIS"],"prefix":"10.1142","volume":"25","author":[{"given":"EDWIN","family":"BEGGS","sequence":"first","affiliation":[{"name":"Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales, UK"}]},{"given":"JOS\u00c9 F\u00c9LIX","family":"COSTA","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049 - 001 Lisboa, Portugal"},{"name":"CMAF Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es Fundamentais, Universidade de Lisboa, Portugal"}]},{"given":"DIOGO","family":"PO\u00c7AS","sequence":"additional","affiliation":[{"name":"Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. Rovisco Pais, 1049 - 001 Lisboa, Portugal"},{"name":"CMAF Centro de Matem\u00e1tica e Aplica\u00e7\u00f5es Fundamentais, Universidade de Lisboa, Portugal"}]},{"given":"JOHN V.","family":"TUCKER","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Swansea University, Singleton Park, Swansea, SA2 8PP, Wales, UK"}]}],"member":"219","published-online":{"date-parts":[[2014,8,7]]},"reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2008.0085"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2008.0412"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39074-6_3"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/ext047"},{"key":"p_7","first-page":"155","volume":"46","author":"Beggs E.","year":"2010","journal-title":"Theory and Decision Library A"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129510000356"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-010-9254-6"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2011.0427"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129511000557"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00086-2"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.09.066"},{"key":"p_18","doi-asserted-by":"publisher","DOI":"10.1007\/BF01886519"},{"issue":"3","key":"p_21","first-page":"193","volume":"5","author":"B.","year":"2009","journal-title":"International Journal of Unconventional Computing"},{"key":"p_22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.64.2354"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90178-3"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1995.1013"},{"key":"p_27","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2004.07.001"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054114400012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:48:27Z","timestamp":1565189307000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054114400012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6]]},"references-count":17,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2014,8,7]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S0129054114400012"],"URL":"https:\/\/doi.org\/10.1142\/s0129054114400012","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6]]}}}