Natural Computing最新文献

The amoebot model (Derakhshandeh et al. in: SPAA ACM, pp 220–222. https://doi.org/10.1145/2612669.2612712, 2014) has been proposed as a model for programmable matter consisting of tiny, robotic elements called amoebots. We consider the reconfigurable circuit extension (Feldmann et al. in J Comput Biol 29(4):317–343. https://doi.org/10.1089/cmb.2021.0363, 2022) of the geometric amoebot model that allows the amoebot structure to interconnect amoebots by so-called circuits. A circuit permits the instantaneous transmission of signals between the connected amoebots. In this paper, we examine the structural power of the reconfigurable circuits. We start with fundamental problems like the stripe computation problem where, given any connected amoebot structure S, an amoebot u in S, and some axis X, all amoebots belonging to axis X through u have to be identified. Second, we consider the global maximum problem, which identifies an amoebot at the highest possible position with respect to some direction in some given amoebot (sub)structure. A solution to this problem can be used to solve the skeleton problem, where a cycle of amoebots has to be found in the given amoebot structure which contains all boundary amoebots. A canonical solution to that problem can be used to come up with a canonical path, which provides a unique characterization of the shape of the given amoebot structure. Constructing canonical paths for different directions allows the amoebots to set up a spanning tree and to check symmetry properties of the given amoebot structure. The problems are important for a number of applications like rapid shape transformation, energy dissemination, and structural monitoring. Interestingly, the reconfigurable circuit extension allows polylogarithmic-time solutions to all of these problems.

Reaction systems are a model of computing aiming to formalize biochemistry by capturing the qualitative relations between the species, and explicitly discarding any accounts of multiplicity. From the point of view of the formal language theory, this situates them in the realm of set rewriting. In this work, we propose a series of extensions of reaction systems to use strings. These extensions form a spectrum in the sense that all of them honor the hallmark features of the original model: the threshold principle and the non-permanency principle. We thoroughly discuss the details of the structure and the behavior of these variants, and commence studying their expressive power by comparing them to some classic models of computing.

The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these machines at larger scales are yet to be fully explored. We introduce and investigate an almost-linear Ising machine, a machine based on a network of analog spins with piece-wise linear coupling. We show that such networks leverage the computational resource similar to that of the semidefinite positive relaxation of the Ising model. We estimate the expected performance of the almost-linear machine and benchmark it on a set of (left{ 0, 1right})-weighted graphs. We show that the running time of the investigated machine scales polynomially (linearly with the number of edges in the connectivity graph). As an example of the physical realization of the machine, we present a CMOS-compatible implementation comprising an array of vertices efficiently storing the continuous spins on charged capacitors and communicating externally via analog current.

Abstract

We study the efficiency of the reaction systems in solving NP-complete problems. Due to the fact that standard reaction systems are qualitative, in order to accomplish our aim, in this paper we consider communicating reaction systems with direct communication extended with duration for resources and a mutual exclusion relation between reactions forbidding two reactions to be used in the same step, in parallel. We show that these systems, working in a non-deterministic way, are powerful enough to provide polynomial-time solutions to the subset sum and SAT problems. We consider a semi-uniform approach by constructing a system for each instance of the subset sum and SAT problems and embedding the parameters into the constructed systems.

Abstract

In this paper we present a model containing modifications to the Signal-passing Tile Assembly Model (STAM), a tile-based self-assembly model whose tiles are capable of activating and deactivating glues based on the binding of other glues. These modifications consist of an extension to 3D, the ability of tiles to form “flexible” bonds that allow bound tiles to rotate relative to each other, and allowing tiles of multiple shapes within the same system. We call this new model the STAM*, and we present a series of constructions within it that are capable of self-replicating behavior. Namely, the input seed assemblies to our STAM* systems can encode either “genomes” specifying the instructions for building a target shape, or can be copies of the target shape with instructions built in. A universal tile set exists for any target shape (at scale factor 2), and from a genome assembly creates infinite copies of the genome as well as the target shape. An input target structure, on the other hand, can be “deconstructed” by the universal tile set to form a genome encoding it, which will then replicate and also initiate the growth of copies of assemblies of the target shape. Since the lengths of the genomes for these constructions are proportional to the number of points in the target shape, we also present a replicator which utilizes hierarchical self-assembly to greatly reduce the size of the genomes required. The main goals of this work are to examine minimal requirements of self-assembling systems capable of self-replicating behavior, with the aim of better understanding self-replication in nature as well as understanding the complexity of mimicking it.

In every matured theory, there is a need to investigate possible relationships between considered objects. To address this issue, it is natural to relate a category with given model of computing. Thanks to such approach, many properties are unified and simplified. In this paper, we investigate how category theory can be used to give a faithful semantics for reaction systems. In particular, we propose and discuss possible approaches to the problem of defining morphisms between reaction systems. We provide the definition of morphism that keeps the behaviour of the original reaction system. Especially, some equivalences of reaction systems are reflected in terms of morphisms. For this purpose we expressed isomorphisms and sections in term of transition systems. Moreover, the accelerating morphism defined in the last section gives a new approach for including time in reaction systems.

We study the problem of determining the size of the smallest tile set that uniquely self-assembles into a given target shape in Winfree’s abstract Tile Assembly Model (aTAM), an elegant theoretical model of DNA tile self-assembly. This problem is also known as the “directed tile complexity” problem. We prove two main results related to the directed tile complexity problem within a variant of the aTAM in which the minimum binding strength threshold (temperature) is set to 1. For our first result, self-assembly happens in a “just-barely 3D” setting, where self-assembling unit cubes are allowed to be placed in the (z=0) and (z=1) planes. This is the same setting in which Furcy, Summers and Withers (DNA 2021) recently proved lower and upper bounds on the directed tile complexity of a just-barely 3D (k times N) rectangle at temperature 1 of (Omega left( N^{frac{1}{k}}right) ) and (Oleft( N^{frac{1}{k-1}}+log Nright) ), respectively, the latter of which does not hold for (k=2). Our first result closes this gap for (k=2) by proving an asymptotically tight bound of (Theta (N)) on the directed tile complexity of a just-barely 3D (2 times N) rectangle at temperature 1. Our proof uses a novel process by which a just-barely 3D assembly sequence is “unfolded” to an equivalent 2D assembly sequence. For our second result, we use the aforementioned lower bound by Furcy, Summers and Withers and a novel process that is complementary-in-spirit to our 3D-to-2D unfolding process, by which we “fold” a 2D tile assembly to an equivalent just-barely 3D assembly to prove a new lower bound on the directed tile complexity of a 2D (k times N) rectangle at temperature 1 of (Omega left( frac{N^{frac{2}{k + (k bmod 2)}}}{k} right) ). For fixed k, our new bound gives a nearly quadratic improvement over, and matches for general even values of (k < frac{log N}{log log N - log log log N}) the state of the art lower bound on the directed tile complexity of a (k times N) rectangle at temperature 1 by Furcy, Summers and Wendlandt (DNA 2019) of (Omega left( N^{frac{1}{k}}right) ). While both of our results represent improvements over previous corresponding state of the art results, the proofs thereof are facilitated by novel examples of reasoning about tile self-assembly happening in 2D (just-barely 3D) as though it is happening in just-barely 3D (2D).

Reaction systems are discrete dynamical systems that simulate biological processes within living cells through finite sets of reactants, inhibitors, and products. In this paper, we study the computational complexity of deciding on the existence of fixed points and attractors in the restricted class of additive reaction systems, in which each reaction involves at most one reactant and no inhibitors. We prove that all the considered problems, that are known to be hard for other classes of reaction systems, are polynomially solvable in additive systems. To arrive at these results, we provide several non-trivial reductions to problems on a polynomially computable graph representation of reaction systems that might prove useful for addressing other related problems in the future.

The use of Cellular Automata (CA) in combination with Learning Automata (LA) has demonstrated effectiveness in handling hard-to-be-solved problems. Due to their capacity to learn and adapt, as well as their inherent parallelism, they can expedite the problem-solving process for a range of problems, such as challenging logic puzzles. One such puzzle is Sudoku, which poses a combinatorial optimization challenge of great difficulty and complexity. In this study, a Sudoku puzzle was represented as an Irregular Learning Cellular Automaton (ILCA), using a reward and penalty algorithm to resolve it. Simulations for an amount of 400 puzzles were performed, while the results demonstrate that the proposed algorithm operates effectively, highlighting the concurrent and learning capabilities of the ILCA structure. Furthermore, two different performance enhancement methods are investigated, namely learning rates method and selective probability reset rule, which are able to increase the initial performance by (26.8%) and to achieve an overall (99.3%) resolution rate.

A distributed reaction system consists of a finite set of reaction systems that either interact with a common environment or interact with each other by communicating products or reactions. A reaction system is a well-known qualitative formal model of interactions between biochemical reactions. A reaction is a triplet of nonempty sets representing chemicals, called the set of reactants, the set of inhibitors, and the set of products. A reaction corresponds to a chemical reaction performed on a set of chemicals, and a reaction system is a finite nonempty set of reactions. In this paper, we examine two variants of distributed reaction systems. We introduce the notion of a distributed reaction system with communication by request (a qDRS for short), where sets of products are communicated between the component reaction systems by queries. First, we show that every qDRS can be represented by a reaction system. After that we compare distributed reaction systems with communication by request to extended distributed reaction systems (EDRSs), models that were introduced in a previous paper. We prove that extended distributed reaction systems, where a context automaton provides input for the component reaction systems, simulate distributed reaction systems with communication by request and distributed reaction systems with communication by request simulate special variants of extended distributed reaction systems. Furthermore, we assign languages to these two variants of distributed reaction systems. We prove that the class of agreement languages of extended distributed reaction systems is equal to the class of languages of nondeterministic multihead finite automata and the agreement language of every distributed reaction system with communication by request is an element of a certain subregular language class.