Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universal Simulation of Directed Systems in the abstract Tile Assembly
  Model Requires Undirectedness   As a mathematical model of self-assembling systems, Winfree's abstract Tile
Assembly Model (aTAM) is a remarkable platform for studying the behaviors and
powers of self-assembling systems. Capable of Turing universal computation, the
aTAM allows algorithmic self-assembly, in which the components can be designed
so that the rules governing their behaviors force them to inherently execute
prescribed algorithms as they combine. Adding to its completeness, the aTAM was
shown to also be intrinsically universal, which means that there exists a
single tile set such that for any arbitrary input aTAM system, that tile set
can be configured into a seed structure which will then cause self-assembly
using that tile set to simulate the input system, capturing its full dynamics
modulo only a scale factor. However, the universal simulator previously given
makes use of nondeterminism in terms of tile types placed in several key
locations when different assembly sequences are followed, even when simulating
a directed system, meaning one that has exactly one unique terminal assembly.
The question then became whether or not that nondeterminism is fundamentally
required. Here, we answer that in the affirmative: the class of directed
systems in the aTAM is not intrinsically universal, meaning there is no
universal simulator for directed systems which itself is always directed. This
provides insight into the role of nondeterminism in self-assembly, which is
itself a fundamentally nondeterministic process. To achieve this result we
leverage powerful results of computational complexity hierarchies, including
tight bounds on both best and worst-case complexities of decidable languages,
to design systems with precisely controllable space resources available to
embedded computations. We also develop novel techniques for designing systems
containing subsystems with disjoint, mutually exclusive computational powers.

22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
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The categories of this paper are: stat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc