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1. Turing Obfuscation

   Wang, Yan; Wang, Shuai; Wu, Dinghao (October 2017, Proceedings of the 13th EAI International Conference on Security and Privacy in Communication Networks (SecureComm 2017))

   Obfuscation is an important technique to protect software from adversary analysis. Control flow obfuscation effectively prevents attackers from understanding the program structure, hence impeding a broad set of reverse engineering efforts. In this paper, we propose a novel control flow obfuscation method which employs Turing machines to simulate the computation of branch conditions. By weaving the orig- inal program with Turing machine components, program control flow graph and call graph can become much more complicated. In addition, due to the runtime computation complexity of a Turing machine, pro- gram execution flow would be highly obfuscated and become resilient to advanced reverse engineering approaches via symbolic execution and concolic testing. We have implemented a prototype tool for Turing obfuscation. Compar- ing with previous work, our control flow obfuscation technique delivers three distinct advantages. 1). Complexity: the complicated structure of a Turing machine makes it difficult for attackers to understand the program control flow. 2). Universality: Turing machines can encode any compu- tation and hence applicable to obfuscate any program component. 3). Resiliency: Turing machine brings in complex execution model, which is shown to withstand automated reverse engineering efforts. Our evalua- tion obfuscates control flow predicates of two widely-used applications, and the experimental results show that the proposed technique can ob- fuscate programs in stealth with good performance and robustness. 

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2. Diffusiophoresis-enhanced Turing patterns

   https://doi.org/10.1126/sciadv.adj2457  

   Alessio, Benjamin M.; Gupta, Ankur (November 2023, Science Advances)

   Turing patterns are fundamental in biophysics, emerging from short-range activation and long-range inhibition processes. However, their paradigm is based on diffusive transport processes that yield patterns with shallower gradients than those observed in nature. A complete physical description of this discrepancy remains unknown. We propose a solution to this phenomenon by investigating the role of diffusiophoresis, which is the propulsion of colloids by a chemical gradient, in Turing patterns. Diffusiophoresis enables robust patterning of colloidal particles with substantially finer length scales than the accompanying chemical Turing patterns. A scaling analysis and a comparison to recent experiments indicate that chromatophores, ubiquitous in biological pattern formation, are likely diffusiophoretic and the colloidal Péclet number controls the pattern enhancement. This discovery suggests that important features of biological pattern formation can be explained with a universal mechanism that is quantified straightforwardly from the fundamental physics of colloids. 

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3. Horizons Protect Church-Turing

   Susskind, Leonard (March 2020, ArXivorg)

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4. Effect of obstructions on growing Turing patterns

   https://doi.org/10.1063/5.0099753  

   Dolnik, Milos; Konow, Christopher; Somberg, Noah H.; Epstein, Irving R. (July 2022, Chaos: An Interdisciplinary Journal of Nonlinear Science)

   We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel–Epstein reaction–diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain, such as walls and slits, and local obstructions, such as small blocks. The pattern formation is significantly affected by the obstructions, leading to novel pattern morphologies. We show that obstructions can induce growth mode switching and disrupt local pattern formation and that these effects depend on the shape and placement of the objects as well as the domain growth rate. This work provides a customizable framework to perform numerical simulations on different types of obstructions and other heterogeneous domains, which may guide future numerical and experimental studies. These results may also provide new insights into biological pattern growth and formation, especially in non-idealized domains containing noise or discontinuities. 

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5. The Turing degrees and Keisler's order

   https://doi.org/10.1017/jsl.2022.63  

   Malliaris, Maryanthe; Shelah, Saharon (March 2024, The Journal of Symbolic Logic)