209 research outputs found
Intrinsic Universality in Self-Assembly
We show that the Tile Assembly Model exhibits a strong notion of universality
where the goal is to give a single tile assembly system that simulates the
behavior of any other tile assembly system. We give a tile assembly system that
is capable of simulating a very wide class of tile systems, including itself.
Specifically, we give a tile set that simulates the assembly of any tile
assembly system in a class of systems that we call \emph{locally consistent}:
each tile binds with exactly the strength needed to stay attached, and that
there are no glue mismatches between tiles in any produced assembly.
Our construction is reminiscent of the studies of \emph{intrinsic
universality} of cellular automata by Ollinger and others, in the sense that
our simulation of a tile system by a tile system represents each tile
in an assembly produced by by a block of tiles in , where
is a constant depending on but not on the size of the assembly
produces (which may in fact be infinite). Also, our construction improves on
earlier simulations of tile assembly systems by other tile assembly systems (in
particular, those of Soloveichik and Winfree, and of Demaine et al.) in that we
simulate the actual process of self-assembly, not just the end result, as in
Soloveichik and Winfree's construction, and we do not discriminate against
infinite structures. Both previous results simulate only temperature 1 systems,
whereas our construction simulates tile assembly systems operating at
temperature 2
Membrane Computing Schema Based on String Insertions
In this note we introduce the notion of a membrane computing schema for
string objects. We propose a computing schema for a membrane network (i.e., tissue-like
membrane system) where each membrane performs unique type of operations at a time
and sends the result to others connected through the channel. The distinguished features
of the computing models obtained from the schema are:
1. only context-free insertion operations are used for string generation,
2. some membranes assume ltering functions for structured objects(molecules),
3. the generating model and accepting model are obtained in the same schema, and
both are computationally universal,
4. several known rewriting systems with universal computability can be reformulated
in terms of membrane computing schema in a uniform manner.
The rst feature provides the model with a simple uniform structure which facilitates a
biological implementation of the model, while the second feature suggests further feasibility
of the model in terms of DNA complementarity.
Through the third and fourth features, one may have a uni ed view of a variety
of existing rewriting systems with Turing computability in the framework of membrane
computing paradigm
Formal models of the extension activity of DNA polymerase enzymes
The study of formal language operations inspired by enzymatic actions on DNA is part of ongoing efforts to provide a formal framework and rigorous treatment of DNA-based information and DNA-based computation. Other studies along these lines include theoretical explorations of splicing systems, insertion-deletion systems, substitution, hairpin extension, hairpin reduction, superposition, overlapping concatenation, conditional concatenation, contextual intra- and intermolecular recombinations, as well as template-guided recombination.
First, a formal language operation is proposed and investigated, inspired by the naturally occurring phenomenon of DNA primer extension by a DNA-template-directed DNA polymerase enzyme. Given two DNA strings u and v, where the shorter string v (called the primer) is Watson-Crick complementary and can thus bind to a substring of the longer string u (called the template) the result of the primer extension is a DNA string that is complementary to a suffix of the template which starts at the binding position of the primer. The operation of DNA primer extension can be abstracted as a binary operation on two formal languages: a template language L1 and a primer language L2. This language operation is called L1-directed extension of L2 and the closure properties of various language classes, including the classes in the Chomsky hierarchy, are studied under directed extension. Furthermore, the question of finding necessary and sufficient conditions for a given language of target strings to be generated from a given template language when the primer language is unknown is answered. The canonic inverse of directed extension is used in order to obtain the optimal solution (the minimal primer language) to this question.
The second research project investigates properties of the binary string and language operation overlap assembly as defined by Csuhaj-Varju, Petre and Vaszil as a formal model of the linear self-assembly of DNA strands: The overlap assembly of two strings, xy and yz, which share an overlap y, results in the string xyz. In this context, we investigate overlap assembly and its properties: closure properties of various language families under this operation, and related decision problems. A theoretical analysis of the possible use of iterated overlap assembly to generate combinatorial DNA libraries is also given.
The third research project continues the exploration of the properties of the overlap assembly operation by investigating closure properties of various language classes under iterated overlap assembly, and the decidability of the completeness of a language. The problem of deciding whether a given string is terminal with respect to a language, and the problem of deciding if a given language can be generated by an overlap assembly operation of two other given languages are also investigated
An Ansatz for undecidable computation in RNA-world automata
In this Ansatz we consider theoretical constructions of RNA polymers into
automata, a form of computational structure. The basis for transitions in our
automata are plausible RNA-world enzymes that may perform ligation or cleavage.
Limited to these operations, we construct RNA automata of increasing
complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent
2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show
how the enzymatic reactions match the logical operations of the RNA automaton,
and describe how biological exploration of the corresponding evolutionary space
is facilitated by the efficient arrangement of RNA polymers into a
computational structure. A critical theme of the Ansatz is the self-reference
in RNA automata configurations which exploits the program-data duality but
results in undecidable computation. We describe how undecidable computation is
exemplified in the self-referential Liar paradox that places a boundary on a
logical system, and by construction, any RNA automata. We argue that an
expansion of the evolutionary space for RNA-2PDA automata can be interpreted as
a hierarchical resolution of the undecidable computation by a meta-system (akin
to Turing's oracle), in a continual process analogous to Turing's ordinal
logics and Post's extensible recursively generated logics. On this basis, we
put forward the hypothesis that the resolution of undecidable configurations in
RNA-world automata represents a mechanism for novelty generation in the
evolutionary space, and propose avenues for future investigation of biological
automata
Intrinsic universality in tile self-assembly requires cooperation
We prove a negative result on the power of a model of algorithmic
self-assembly for which it has been notoriously difficult to find general
techniques and results. Specifically, we prove that Winfree's abstract Tile
Assembly Model, when restricted to use noncooperative tile binding, is not
intrinsically universal. This stands in stark contrast to the recent result
that, via cooperative binding, the abstract Tile Assembly Model is indeed
intrinsically universal. Noncooperative self-assembly, also known as
"temperature 1", is where tiles bind to each other if they match on one or more
sides, whereas cooperative binding requires binding on multiple sides. Our
result shows that the change from single- to multi-sided binding qualitatively
improves the kinds of dynamics and behavior that these models of nanoscale
self-assembly are capable of. Our lower bound on simulation power holds in both
two and three dimensions; the latter being quite surprising given that
three-dimensional noncooperative tile assembly systems simulate Turing
machines. On the positive side, we exhibit a three-dimensional noncooperative
self-assembly tile set capable of simulating any two-dimensional noncooperative
self-assembly system.
Our negative result can be interpreted to mean that Turing universal
algorithmic behavior in self-assembly does not imply the ability to simulate
arbitrary algorithmic self-assembly processes.Comment: Added references. Improved presentation of definitions and proofs.
This article uses definitions from arXiv:1212.4756. arXiv admin note: text
overlap with arXiv:1006.2897 by other author
The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square
In this paper we define the Dupled abstract Tile Assembly Model (DaTAM),
which is a slight extension to the abstract Tile Assembly Model (aTAM) that
allows for not only the standard square tiles, but also "duple" tiles which are
rectangles pre-formed by the joining of two square tiles. We show that the
addition of duples allows for powerful behaviors of self-assembling systems at
temperature 1, meaning systems which exclude the requirement of cooperative
binding by tiles (i.e., the requirement that a tile must be able to bind to at
least 2 tiles in an existing assembly if it is to attach). Cooperative binding
is conjectured to be required in the standard aTAM for Turing universal
computation and the efficient self-assembly of shapes, but we show that in the
DaTAM these behaviors can in fact be exhibited at temperature 1. We then show
that the DaTAM doesn't provide asymptotic improvements over the aTAM in its
ability to efficiently build thin rectangles. Finally, we present a series of
results which prove that the temperature-2 aTAM and temperature-1 DaTAM have
mutually exclusive powers. That is, each is able to self-assemble shapes that
the other can't, and each has systems which cannot be simulated by the other.
Beyond being of purely theoretical interest, these results have practical
motivation as duples have already proven to be useful in laboratory
implementations of DNA-based tiles
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