English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

As a mathematical model of self-assembling systems, Winfree's abstract TileAssembly Model (aTAM) is a remarkable platform for studying the behaviors andpowers of self-assembling systems. Capable of Turing universal computation, theaTAM allows algorithmic self-assembly, in which the components can be designedso that the rules governing their behaviors force them to inherently executeprescribed algorithms as they combine. Adding to its completeness, the aTAM wasshown to also be intrinsically universal, which means that there exists asingle tile set such that for any arbitrary input aTAM system, that tile setcan be configured into a seed structure which will then cause self-assemblyusing that tile set to simulate the input system, capturing its full dynamicsmodulo only a scale factor. However, the universal simulator previously givenmakes use of nondeterminism in terms of tile types placed in several keylocations when different assembly sequences are followed, even when simulatinga directed system, meaning one that has exactly one unique terminal assembly.The question then became whether or not that nondeterminism is fundamentallyrequired. Here, we answer that in the affirmative: the class of directedsystems in the aTAM is not intrinsically universal, meaning there is nouniversal simulator for directed systems which itself is always directed. Thisprovides insight into the role of nondeterminism in self-assembly, which isitself a fundamentally nondeterministic process. To achieve this result weleverage powerful results of computational complexity hierarchies, includingtight bounds on both best and worst-case complexities of decidable languages,to design systems with precisely controllable space resources available toembedded computations. We also develop novel techniques for designing systemscontaining subsystems with disjoint, mutually exclusive computational powers.

Universal Simulation of Directed Systems in the abstract Tile Assembly Model Requires Undirectedness