Stochastic Turing Machines obtained from ensembles of Wang tiling

Stochastic Turing Machines obtained from ensembles of Wang tiling | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 13 September 2025 V1 Latest version Share on Stochastic Turing Machines obtained from ensembles of Wang tiling Authors : cenap Ozel , Patrick Linker , and Mustafa Tahsin Yilmaz 0000-0002-5385-8858 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175775048.80018145/v1 226 views 93 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We propose a novel generalization of the saddle-point method for evaluating high-dimensional oscillatory integrals, particularly arising in contexts such as statistical field theories and computational complexity models. Our method builds upon the recursive insertion of unity via delta functionals, enabling a multistage approximation that adapts to the structure of critical points. In particular, this method is applied to a path-integral formulation of a Random Turing Machine based on Wang tile ensembles, capturing stochastic computational evolution. We demonstrate that our approach, while conservative in assumptions, exhibits superior accuracy and depth when applied to integrals with strongly fluctuating integrands. Furthermore, we show that our generalized method can be hybridized with resurgence techniques at the leaf nodes of the critical-point tree. This allows the method to interpolate between traditional saddle-point methods and modern transseries expansions. The theoretical underpinnings are situated alongside recent developments by Linker and Ozel (2025), who provided a formal analysis of generalized saddle-point approximations in multidimensional contexts. Supplementary Material File (turing_machines last.pdf) Download 210.79 KB Information & Authors Information Version history V1 Version 1 13 September 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords equiprobability saddle point approximations statistical field theories stochastic turing machines wang tiling Authors Affiliations cenap Ozel King Abdulaziz University View all articles by this author Patrick Linker Technische Universitat Darmstadt Fachbereich Mathematik View all articles by this author Mustafa Tahsin Yilmaz 0000-0002-5385-8858 [email protected] King Abdulaziz University View all articles by this author Metrics & Citations Metrics Article Usage 226 views 93 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation cenap Ozel, Patrick Linker, Mustafa Tahsin Yilmaz. Stochastic Turing Machines obtained from ensembles of Wang tiling. Authorea . 13 September 2025. DOI: https://doi.org/10.22541/au.175775048.80018145/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.175775048.80018145/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fef680a8ba2300f',t:'MTc3OTMyMjczMw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();