Model Checking Temporal Logic Formulas Using Sticker Automata

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method

Towards the Design of Heuristics by Means of Self-Assembly

The current investigations on hyper-heuristics design have sprung up in two different flavours: heuristics that choose heuristics and heuristics that generate heuristics. In the latter, the goal is to develop a problem-domain independent strategy to automatically generate a good performing heuristic for the problem at hand. This can be done, for example, by automatically selecting and combining different low-level heuristics into a problem specific and effective strategy. Hyper-heuristics raise the level of generality on automated problem solving by attempting to select and/or generate tailored heuristics for the problem at hand. Some approaches like genetic programming have been proposed for this. In this paper, we explore an elegant nature-inspired alternative based on self-assembly construction processes, in which structures emerge out of local interactions between autonomous components. This idea arises from previous works in which computational models of self-assembly were subject to evolutionary design in order to perform the automatic construction of user-defined structures. Then, the aim of this paper is to present a novel methodology for the automated design of heuristics by means of self-assembly

The Impacts of Dimensionality, Diffusion, and Directedness on Intrinsic Cross-Model Simulation in Tile-Based Self-Assembly

Algorithmic self-assembly occurs when components in a disorganized collection autonomously combine to form structures and, by their design and the dynamics of the system, are forced to intrinsically follow the execution of algorithms. Motivated by applications in DNA-nanotechnology, theoretical investigations in algorithmic tile-based self-assembly have blossomed into a mature theory with research strongly leveraging tools from computability theory, complexity theory, information theory, and graph theory to develop a wide range of models and to show that many are computationally universal, while also exposing a wide variety of powers and limitations of each. In addition to computational universality, the abstract Tile-Assembly Model (aTAM) was shown to be intrinsically universal (FOCS 2012), a strong notion of completeness where a single tile set is capable of simulating the full dynamics of all systems within the model; however, this result fundamentally required non-deterministic tile attachments. This was later confirmed necessary when it was shown that the class of directed aTAM systems, those in which all possible sequences of tile attachments eventually result in the same terminal assembly, is not intrinsically universal (FOCS 2016). Furthermore, it was shown that the non-cooperative aTAM, where tiles only need to match on 1 side to bind rather than 2 or more, is not intrinsically universal (SODA 2014) nor computationally universal (STOC 2017). Building on these results to further investigate the impacts of other dynamics, Hader et al. examined several tile-assembly models which varied across (1) the numbers of dimensions used, (2) restrictions imposed on the diffusion of tiles through space, and (3) whether each system is directed, and determined which models exhibited intrinsic universality (SODA 2020). Such results have shed much light on the roles of various aspects of the dynamics of tile-assembly and their effects on the universality of each model. In this paper we extend that previous work to provide direct comparisons of the various models against each other by considering intrinsic simulations between models. Our results show that in some cases, one model is strictly more powerful than another, and in others, pairs of models have mutually exclusive capabilities. This direct comparison of models helps expose the impacts of these three important aspects of self-assembling systems, and further helps to define a hierarchy of tile-assembly models analogous to the hierarchies studied in traditional models of computation

Problems in Algorithmic Self-assembly and a Genetic Approach to Patterns

As it becomes increasingly harder to make transistors smaller, replacements for traditional silicon computers become sought after. To study the computing power of these potential computers, various theoretical models have been proposed, such as the abstract Tile Assembly Model (aTAM) and chemical reaction networks (CRNs). This thesis compiles research in various models such as the aTAM, Tile Automata, and CRNs. This work shows an investigation of covert computation in the aTAM and an evolutionary algorithm to approximate solutions to the pattern self-assembly tile set synthesis (PATS) problem. Next, optimal state complexity for building squares in Tile Automata is shown along with a Tile Automata simulation of the staged assembly model (SAM). Lastly, reachability for restricted general CRNs, reachability for feed-forward CRNs, and reachability for Void and Autogenesis CRNs are shown to be in various complexity classes

On Undecidable Dynamical Properties of Reversible One-Dimensional Cellular Automata

Cellular automata are models for massively parallel computation. A cellular automaton consists of cells which are arranged in some kind of regular lattice and a local update rule which updates the state of each cell according to the states of the cell's neighbors on each step of the computation. This work focuses on reversible one-dimensional cellular automata in which the cells are arranged in a two-way in_nite line and the computation is reversible, that is, the previous states of the cells can be derived from the current ones. In this work it is shown that several properties of reversible one-dimensional cellular automata are algorithmically undecidable, that is, there exists no algorithm that would tell whether a given cellular automaton has the property or not. It is shown that the tiling problem of Wang tiles remains undecidable even in some very restricted special cases. It follows that it is undecidable whether some given states will always appear in computations by the given cellular automaton. It also follows that a weaker form of expansivity, which is a concept of dynamical systems, is an undecidable property for reversible one-dimensional cellular automata. It is shown that several properties of dynamical systems are undecidable for reversible one-dimensional cellular automata. It shown that sensitivity to initial conditions and topological mixing are undecidable properties. Furthermore, non-sensitive and mixing cellular automata are recursively inseparable. It follows that also chaotic behavior is an undecidable property for reversible one-dimensional cellular automata.Siirretty Doriast

On bounded Wang tilings

Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging applications in materials engineering, we consider the bounded version of the tiling problem and offer four integer programming formulations to construct valid or nearly-valid Wang tilings: a decision, maximum-rectangular tiling, maximum cover, and maximum adjacency constraint satisfaction formulations. To facilitate a finer control over the resulting tilings, we extend these programs with tile-based, color-based, packing, and variable-sized periodic constraints. Furthermore, we introduce an efficient heuristic algorithm for the maximum-cover variant based on the shortest path search in directed acyclic graphs and derive simple modifications to provide a $1/2$ approximation guarantee for arbitrary tile sets, and a $2/3$ guarantee for tile sets with cyclic transducers. Finally, we benchmark the performance of the integer programming formulations and of the heuristic algorithms showing that the heuristics provides very competitive outputs in a fraction of time. As a by-product, we reveal errors in two well-known aperiodic tile sets: the Knuth tile set contains a tile unusable in two-way infinite tilings, and the Lagae corner tile set is not aperiodic

Adaptive Multi-Functional Space Systems for Micro-Climate Control

This report summarizes the work done during the Adaptive Multifunctional Systems for Microclimate Control Study held at the Caltech Keck Institute for Space Studies (KISS) in 2014-2015. Dr. Marco Quadrelli (JPL), Dr. James Lyke (AFRL), and Prof. Sergio Pellegrino (Caltech) led the Study, which included two workshops: the first in May of 2014, and another in February of 2015. The Final Report of the Study presented here describes the potential relevance of adaptive multifunctional systems for microclimate control to the missions outlined in the 2010 NRC Decadal Survey. The objective of the Study was to adapt the most recent advances in multifunctional reconfigurable and adaptive structures to enable a microenvironment control to support space exploration in extreme environments (EE). The technical goal was to identify the most efficient materials, architectures, structures and means of deployment/reconfiguration, system autonomy and energy management solutions needed to optimally project/generate a micro-environment around space assets. For example, compact packed thin-layer reflective structures unfolding to large areas can reflect solar energy, warming and illuminating assets such as exploration rovers on Mars or human habitats on the Moon. This novel solution is called an energy-projecting multifunctional system (EPMFS), which are composed of Multifunctional Systems (MFS) and Energy-Projecting Systems (EPS)

Automated evolutionary design of self-assembly and self-organising systems

Self-assembly and self-organisation are natural construction processes where the spontaneous formation of aggregates emerges throughout the progressive interplay of local interactions among its constituents. Made upon cooperative self-reliant components, self-assembly and self-organising systems are seen as distributed, not necessarily synchronous, autopoietic mechanisms for the bottom-up fabrication of supra-structures. The systematic understanding of how nature endows these autonomous components with sufficient ''intelligence'' to combine themselves to form useful aggregates brings challenging questions to science, answers to which have many potential applications in matters of life and technological advances. It is for this reason that the investigation to be presented along this thesis focuses on the automated design of self-assembly and self-organising systems by means of artificial evolution. Towards this goal, this dissertation embodies research on evolutionary algorithms applied to the parameters design of a computational model of self-organisation and the components design of a computational model of self-assembly. In addition, an analytical assessment combining correlation metrics and clustering, as well as the exploration of emergent patterns of cooperativity and the measurement of activity across evolution, is made. The results support the research hypothesis that an adaptive process such as artificial evolution is indeed a suitable strategy for the automated design of self-assembly and self-organising systems where local interactions, homogeneity and both stochastic and discrete models of execution play a crucial role in emergent complex structures