DNA Tiling for Digital Evolvable Hardware

Pauline C. Haddow and Vinay Kumar GautamCRAB Lab, Gemini Centre for Applied AI

Department of Computer Science and Informatics

Norwegian University of Science and Technology (NTNU)

Email: pauline@idi.ntnu.no, vkgautam@idi.ntnu.no

Abstract—Platforms for digital evolvable hardware have beendominated by reconfigurable chips in the form of Field Pro-grammable Gate Arrays (FPGA). Despite a number of successeswith such a computation medium for evolving digital designs, itis commonly accepted that technological constraints are limitingthe potential inherent in such evolutionary techniques. Thus, itis desirable to investigate potential technologies that enable ex-ploitation of the technology itself, despite a digital computationalmodel. This paper presents a preliminary investigation into DNAtiling as a platform for digital Evolvable Hardware. Considerationis given to ways in which such a biological medium could beadapted so as to offer a platform for digital design, exploitableand tunable through the application of an evolutionary algorithm,enabling a digital design to emerge. The solutions proposedconsider two different forms of DNA tiling — Algorithmic andLogical. Further, the proposed solutions are compared to FPGAtechnology in the light of the requirements that evolutionaryapproaches place on the underlying technology and challengeshighlighted provide a guideline for further investigation into theviability of such a platform.

Keywords—DNA tiling, Self-assembly, Evolution, EvolvableHardware, Digital Design

I. INTRODUCTION

Evolvable Hardware (EHW) [1] is often regarded as abottom-up design process where a genotype description pro-vides a mapping between a potential solution (digital design)and the computational model of the underlying technology.The correct design solution then emerges as a result of theevolutionary process and provides either an electronic designin hardware or a simulated design/device solution in a real-istic simulator. As such, the approach frees itself from thetraditional design methodology with its inherent constraints.However, technological constraints still prevail.

The focus of the Evolvable Hardware community hasmainly been directed towards traditional technology platformsand applying evolutionary techniques (as well as other bio-inspired techniques) to evolve new or optimised designs andthus prove the worth of Evolvable Hardware as a designtechnique. Although successes have been achieved, EvolvableHardware has clear scalability issues, one solution being toconsider other platforms more attuned to the requirements thatevolutionary techniques place on the underlying platform.

A number of researchers have created EHW technologyplatforms [2], [3] so as to reduce today’s technological con-straints. Others have allowed evolution to exploit the under-lying technology [1], that is below that of the computationalmodel of the technology platform. Newer materials for EHWhave been investigated including the pioneering work of Hard-ing and Miller into liquid crystal [4].

In this work, DNA tiling is investigated as a platformfor digital EHW. DNA tiling is a newer technique at themolecular scale for structural solutions (nano applications) aswell as computational solutions. Two main tiling techniqueshave emerged in recent years — algorithmic [5] and logicalDNA tiling [6]. Logical DNA tiling, as the name suggests,has been designed specifically towards the traditional conceptof logic gates. On the other hand, some initial investigationsinto algorithmic tiling as the basis for circuit design have alsobeen conducted [6], including work into ways of introducinginputs [7], not originally part of algorithmic DNA tiling andfundamental to circuit design.

A key strength of DNA tiling is the bottom up approach tocomputation. As such, evolutionary techniques may exploit thecharacteristics of the underlying technology — the DNA itself,rather than an abstract model of the technology as in today’sdigital EHW platform — the Field Programmable Gate Array(FPGA).

The paper is structured as follows: Evolvable Hardware ispresented in section II and in section III, DNA tiling is intro-duced. Sections IV and V present the two different approachesto DNA tiling computation. Section VI proposes two potentialEHW platforms based on the two DNA tiling approaches.Further, in section VII, the requirements that evolutionarytechniques place on the underlying technology are discussedin the light of the characteristics of FPGA technology and theproposed DNA tiling technologies. Section VIII concludes thepaper, highlighting some of the challenges inherent in DNAtiling as a platform for EHW that need to be addressed beforethe viability of such a platform may truly be assessed.

II. EVOLVABLE HARDWARE

Evolvable Hardware (EHW) was originally proposed asthe application of evolutionary techniques to the design ofelectronic solutions on programmable electronics, includingboth digital (FPGA) and analogue (FPAA) technologies. Akey difference to traditional techniques being the emergenceof the evolved solution, rather than the design of the solution.In recent years the field has expanded to include a numberof other bio-inspired techniques and combinations thereof andthe evolution of platform solutions as well as designs.

EHW may be classified into two main categories: Evolv-able Hardware Design and Adaptive Hardware [8]. Such aclassification refers to whether evolution is applied to thecreation of a static solution or whether evolution is appliedto an adaptive design, where the design may change itsfunctionality or structure due to environmental influences.

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Three forms of evolvable design approaches may be seen,that of extrinsic, intrinsic and complete hardware evolution(on-chip evolution). In extrinsic, the evolutionary process isconducted in software and the final evolved design applied toconfigure/program the hardware. Intrinsic implies that everyindividual is tested in real hardware. Complete hardwareevolution, on the other hand, implies that both the evolutionaryprocess and the evolving design are implemented on thehardware platform.

FPGA technology has been a driving force within evolvablehardware for digital design. Figure 1 illustrates a standard evo-lutionary cycle for both the case of a) extrinsic evolution and b)intrinsic evolution. Unlike DNA tiling, it is important to notethat at the start of the evolutionary process, the architecture ofthe FPGA architecture is available. The evolutionary processworks on a population of genomes and for the case of extrinsicevolution (a), fitness evaluation of individuals is conducted ona simulation platform. In the case of intrinsic evolution (b),each individual is tested on the FPGA itself.

evolution

Simulationplatform (a)

(b)

Evolved hardware design

Fig. 1. Evolvable Hardware in FPGA (a) extrinsic evolution (b) intrinsicevolution

III. DNA TILING

DNA tiling [5] is a newer form of DNA computinginvolving self-assembly of DNA molecules, based on themathematical tiling theory of Wang [9]. These DNA molecules,also known as DNA tiles [10], consist of four or five shortlength (15-50 nucleotides) single stranded DNA (ss-DNA)molecules, synthesised for a given DNA tile design. Figure 2illustrates the construction of a tile with four strands. As shownin (a), each ss-DNA consists of a sequence of nucleotides (A,T, G, C). The tiles self-assemble through the bonding of thesess-DNAs at room temperature. The bonding process occurswhen two complimentary strands meet and their base pairs: A-T and G-C, bind. Any left-over bases from each of the bondedstrands form a sticky end(s) — as shown in (b). As the termimplies, this end is available to ”stick” or bond to anotherstrand. DNA tiles, in general, are square shaped structures

where sticky-ends are represented by their respective squareedges — as illustrated in (c).

Fig. 2. DNA tile (a) four ss-DNA (b) assembled DNA tile (c) abstractrepresentation

In DNA tiling, a single DNA tile may be designed asa simple computational unit, where the ss-DNAs within thetile are designed so as to provide an encoding of inputsand outputs at the sticky-ends and some form of functionfrom inputs to outputs. Large numbers of DNA tiles may beself-assembled via sticky-end associations, sticking outputs toinputs and providing a large parallel computation platform.Although inputs and outputs clearly exist, a challenge is tofind ways in which external inputs may be introduced to theplatform and outputs extracted.

The DNA strands can be designed by state-of-the-art au-tomation tools such as Tilesoft [11]. Further, the tile self-assembly process itself can be realistically simulated usingsimulators such as kinetic Tile Assembly Model (kTAM) [5].In recent years, the availability of such simulation tools and thereduced cost and thus availability of such DNA molecules, hasincreased the viability of such a technology for investigationas a platform for Evolvable Hardware.

Further investigation into a potential DNA tiling platformrequires consideration as to which tiling technique would beapplied. Two main tiling techniques have emerged in recentyears — algorithmic and logical DNA tiling, and either tech-nique could provide the basis for a potential EHW medium.As such, both techniques are considered in this work.

IV. ALGORITHMIC DNA TILING

Winfree [5] introduced DNA tiling for algorithmic com-putation. To perform an algorithmic computation, a set of tiletypes is required. Generally, for quarter plane DNA tiling, thetile set consists of a single seed tile (S), boundary tiles (X, Y)and rule tiles. It should be noted that DNA structures otherthan quarter plane may also be created.

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In designing a tile set, exact quantities of boundary tilesand rule tiles are not necessary or in fact realistic due tothe emergent nature of the DNA tiling process. Instead, largequantities of such tiles should be made available. Each tiletype has DNA sticky-ends of a specific nucleotide sequenceand length (representing the binding strength).

The seed tile is added to a soup of DNA tiles, includ-ing the boundary and rule tiles. The process of growinga computational architecture starts from the seed tile andproceeds as boundary and rule tiles bond to the growingassembly. There is no predefined ordering as to which tilesmay bond at a particular time, rather bonding depends on theneighbouring free tiles, the available sticky-ends at the freeslot(s) and their strengths, as well as other natural factorssuch as temperature. Thus the computational structure (2D tilestructure) and functional/structural design emerges from thesoup of free tiles.

The technology platform is thus the tile sets themselves,designed to provide an architecture of inherent computationthrough tile bonding. The DNA molecules forming the strandsof a given tile are encoded so as to represent computationrules and the sticky-ends encoded as computation values e.g.0 or 1. Therefore, the adjacent relations of tiles in the finalsuperstructure are controlled by the encoded computing rules,providing a computational architecture.

Algorithmic DNA tiling has been shown to be Turinguniversal [12]. A technological platform based on AlgorithmicDNA tiling should, in principle, be applicable to any function— digital design, given a finite set of tiles. However, for agiven function a suitable set of tiles is needed, a challengethat may be addressed by evolutionary techniques, as discussedfurther in section VI.

A. Example of Algorithmic DNA Computation

A popular example of algorithmic DNA computation is thesierpinski triangles [13]. The tile set, as illustrated in figure 3,comprises of a seed tile, two boundary tiles and four ruletiles. These tiles are based on DNA Double crossover (DX)molecules [10], having single strand DNA sticky-ends. Thelength of these sticky-ends represents the glueing (bonding)strengths — marked 0, 1 or 2. To achieve computation, theSouth and West edges of all tile types are designed as inputsand the North and East as outputs. As stated, computationalinformation may be encoded in the sticky-ends, which in thiscase are the logical values 1 and 0 — illustrated by the abstractrepresentation: black 1 and gray 0 half circles. The encodingof these sticky ends further ensures that bonding creates acomputational flow of information, equivalent to a 2-inputXOR gate and restricts bonding to sticky-ends of the correctstrength i.e. length (encoded sequence length).

V. LOGICAL DNA TILING

Logical DNA tiling [14] was, as the name suggests, origi-nally proposed to implement logic gates using DNA tiles. Assuch, in theory, there already exists a potential logical DNAtechnology. However, no consensus has been found as to whichemerging approach should be applied. Two approaches areconsidered herein.

Fig. 3. Algorithmic DNA tiling : (a) Sierpinski tile set (b)Assembledcomputational structure

The role of sticky-ends is the same as in algorithmicDNA tiling with respect to the stable bonding that occursonly between two complementary and equal strength (length)sticky-ends. However, in contrast to DNA tiling, the stickyends do not encode digital information. Instead the tile itselfencodes the digital information.

In the first approach [14], each tile represents a bit (0or 1) of information. When two such tiles (inputs) bindselectively to a third tile (output) then this tiling assembly(supertile) represents a logic gate (XOR, AND, OR NOT etc.).Therefore, in principle, a matrix of such logic gates can bedesigned to implement a DNA tiling circuit. However, thiswould be limited to combinational designs only, because ofthe asynchronous nature of DNA tiling.

In the second approach [6], a logic gate is a single tileencoded with the required inputs and outputs. That is an ss-DNA within the tile encodes the two inputs and a further ss-DNA encodes the output. Further, if, for example, an 8-bitoperation were sought, eight tiles would be needed. In addition,for either a single logic gate or an x-bit logic gate, two cornertiles act as support tiles, sandwiching in the tile(s) as a logicalentity. The x-bit array of tiles forming the x-bit logical gatecan compute an output based on a given input in parallel forany X, thus exploiting the inherent parallelism of the DNAcomputation and the assembled structure.

Currently, this approach seems applicable to designs havinglogic gates in a single layer because the output of logic gateis encoded within the logic tile which makes it inaccessibleto the next layer of logic gates. However, there are otherapproaches proposed [7] and [14] that could address thislimitation enabling designs with multilayer hierarchy of logicgates.

In both approaches, outputs are extracted by the applicationof suitable enzymes that cut the self-assembled reporter strandrunning through all the input and output tiles.

A. Example of Logical DNA tiling

Hao Yan et al. [6] demonstrated XOR logic computation,applying logical DNA tiling in the form of the single tile logicgate. A DNA tile is assembled out of five ss-DNA strands, asillustrated in figure 4. As shown in (a), there are two longstrands — one at the top and one at the bottom. Further thereis a circular strand and two short strands. The upper longDNA strand encodes the two input bits whilst the lower long

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DNA strand encodes the logical output — see (c). Further,corner tiles LX and RX are designed to assemble with thelogic tile and consist of 4-arm junction tiles — see (b). Suchtiles when assembled with the logic gate, enable ligation of theupper and lower strands together with the connected strands ofcorner tiles — see (d), resulting in a continuous DNA strandconsisting of both the input and output bits of the logic gate.Further, output of the logic gate can be extracted by selectivelycutting the continuous DNA strand using enzyme cutters. Toperform the XOR operation, four logic tiles and two cornertiles are required — see (e).

o1 o2 o3 o4

I12 I11 I21 I22 I31 I32 I41 I42LX RX

I1

o

I2 LX RX

Fig. 4. XOR logic gate implementation using DNA tiles (a) XOR logic gatetile, (b) Four arm junction DNA tile used as corner tiles (LX and RX),(c)Abstract representation of the logic tile and the corner tiles, (d) assembled1-bit XOR logic along with corner tiles and (e) 4-bit pairwise XOR tile array

VI. PROPOSED DNA TILING EHW TECHNOLOGIES

Having two potential DNA technologies for EHW, thissection will consider how evolutionary techniques might beapplied to DNA tiling technologies.

A. EHW: Algorithmic DNA tiling

As stated, Algorithmic DNA tiling consists of a set of tileswith computing rules encoded in their corresponding sticky-ends. When considering an evolutionary approach to the designof such tiles, imagine a population of such tile sets where thegenotype consists of the required tile types as well as providingfor the encoding of the number of sticky-ends, their respectivelengths and nucleotide content for a given tile type.

As illustrated in figure 5, evolution would run on a pop-ulation of such individuals, testing the resulting tile sets insimulation i.e. allowing the tile sets to grow into tile structures,and evaluating the structures. The best solution would providea suitable tile set for the sought application, consisting of alist of the required DNA molecules.

In figure 5, two potential functions are highlighted. In thesierpinski triangles — described in section IV-A, there arethree different tile types and the emerging structure reflectstheir types, with a corner seed tile and the rule tiles creating

Fig. 5. Evolving hardware in algorithmic DNA tiling

the emergent pattern, bordered by the border tiles. In thesecond example, a functional structure is presented. Againthe evolved set of tiles provides a seed tile and border tilesand rule tiles. When the tile structure grows, the seed tilesand border tiles, similar to the sierpinski triangle, provide astarting tile and border tiles to the solution. However the ruletiles, in cooperation with the border tiles ensure a resulting tilepattern forming a 4-bit binary counter computation. What isimportant to note is that although we have two examples thatillustrate a structural and functional goal respectively, we haveno example showing how to create a function with externalinputs and extraction of outputs.

The algorithmic DNA tiling approach does not currentlyinvolve any form of external inputs or outputs. However, inthe work of [7], pre-assembled structures were applied insteadof a single seed tile so as to provide a more guided start tothe further growth of the emergent structure i.e. restricting thepotential growth paths. It is proposed that such pre-assembledstructures — consisting of a seed tile and a few boundary tiles,could provide a way to encode for external inputs.

A further issue is how to extract outputs. After allowingthe DNA tile structure to grow and stabilise, it is proposed toextract outputs from the outer tiles i.e. those at the front of theassembly. Using established techniques such as ligation, thess-DNA of these outer tiles may be joined together to form achain. The resulting long ss-DNA, may then be extracted todetect the output values.

Considering the role of evolution it is clear that preliminaryexperiments might involve allowing evolution to search in thespace expressed by a genome, limited by available tile types.Despite such a limitation, this would enable exploration of newefficient tile sets for existing or new applications. However,and perhaps more importantly, evolution may also be appliedto the design of the tiles themselves i.e. the exploration ofnew tile types and suitable tile sets for an expanded range ofapplications or more efficient solutions to existing applications.

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In either case, evolved tile sets provide the specification forwet-lab experiments that may confirm the simulated results.

B. EHW: Logical DNA tiling

In traditional design, a function described at the gate-level can be implemented using different sets of logic gates,where the choice depends on the designer and efficiencysought. Similarly, in logical DNA tiling, a design could beimplemented by different sets of X-bit DNA logic gates andcorner tiles. Figure 6 provides an example of Logical DNAtiling based on the approach that each tile represents a logicalgate equivalent i.e. encoding both inputs and the output withina single tile. It should be noted, however, that evolution maysimilarly be applied to the other approaches.

S1

Evolved tile set-I

SC

S2

Evolved tile set-II

Evolved set of tiles

output

Adder2 bit parallel XOR logic

Fig. 6. Evolving hardware in logical DNA tiling

As shown, evolution would need to search for a set of logictiles and corner tiles. In this case, the genome might encodethe parameters (sticky-end length, nucleotide content) of eachlogic gate tile and respective corner tiles required, along withthe concentrations of the logic gates and corner tiles.

The evolutionary process would be similar to that of thealgorithmic tile set process, evaluating evolving tile sets insimulation before presenting the final evolved tile set as a spec-ification for wet lab implementation. However, in contrast tothe Algorithmic approach, the evolved tile set would explicitlydefine the required number of tiles of each type.

The evolved tile set-I (adder circuit), illustrated in figure 6,consists of one copy of the XOR gate tile (top-middle) and ofthe AND gate tile (bottom-middle) as well as two corner tilepairs and outputs S and C. However, in the evolved tile set-II(2- bit parallel XORing circuit), two copies of the XOR gatetile (middle tow tiles) are selected together with one copy ofa pair of corner tiles and outputs S1 and S2.

VII. REQUIREMENTS AND CHARACTERISTICS

We have proposed ways in which DNA tiling might be ableto be applied as an EHW platform. However, to achieve anunderstanding of the suitability of a technology as a platformfor evolvable hardware, it is important to consider the require-ments that an evolutionary approach places on the underlyingtechnology [15]. That is, there needs to exist a potentialmapping between such requirements and the characteristicsof the underlying technology. As stated, in this work thefocus is on digital design and the requirements that such acomputation model place on the mapping are also taken intoaccount. However, in evaluating how well DNA tiling meetssuch characteristics it is important to also consider today’ssolutions so as to see where DNA tiling might offer advantagesor disadvantages. To this end DNA tiling is compared to FPGAtechnology.

A. Configurable Platform

As stated, in Evolvable Hardware three forms of evolvabledesign approaches may be seen — extrinsic, intrinsic andcomplete hardware evolution. For extrinsic, the underlyingtechnology needs to be able to be configured/programmed.However, since it is a one-off programming then the require-ment of reconfigurability is not applicable for an EvolvableHardware Design. For Adaptive Hardware, on the other hand,environmental influences need to be able to trigger eitherevolution of a refined design or selection of a replacementdesign. Thus, even in extrinsic hardware, some form of recon-figurability may be required.

Intrinsic, places a strong requirement on reconfigurabilitywhether Evolvable Hardware Design or Adaptive Hardware issought so as to test each individual on the actual hardware.The third approach, complete hardware evolution, also placesa strong requirement of reconfiguration and most commonlyself-reconfiguration of the underlying technology. Althoughself-reconfiguration is available in today’s FPGAs, the use ofsuch features is still poorly supported and thus hard to achieve.

DNA tiling technology, whether logical or algorithmic isinherently an extrinsic approach. There is no generic hardwareavailable, as in FPGA technology. Instead the technologicalarchitecture is designed in parallel to the design solution itself.An integrated design process results in a description of thematerials — DNA required, for the architecture and designedsolution.

A more generic DNA tiling technology, although notcurrently available, could theoretically be designed, providingthe potential for an intrinsic approach with similar benefitsto that of FPGA technology with respect to more realisticevaluations. However, many issues exist, not least the costversus generality trade-off. For the near future, however, anyevolutionary experimentation with DNA tiling is expected tobe conducted through extrinsic experiments.

In logical DNA tiling, the bonding of tiles and supertilesmay be released by temperature control i.e. the process isreversable, rather than reconfigured. With today’s wet-labtechniques, the DNA strands may be reused within the soupbut may not be individually extracted and reused seperatelyin other experiments. However, through the application of

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temperature and suitable support tiles, the soup of DNA tilesmay be reused — reconfigured.

B. Digital Design

Digital design does not exploit the full potential of theunderlying technology but instead includes an abstraction ofthe underlying technology and a methodology to control it.The digital design methodology places an assumption on theunderlying technology that a directed message may be sentfrom one output gate to a designated input gate over a fixedpath [16]. Further, a correct value may be detected and amethodology applied — synchronous or asynchronous, thatensures that correct (stable) values are transmitted within thedesign. Further, the value transmitted will be either a 1 (overa given threshold) or a 0 (under a given threshold).

In FPGA technology, the architecture of the technology,provides for configuration of directed paths from outputs ofa given component to inputs of another component. Further,connections exist which connect the inputs of the designsolution to the outputs, thus creating a physical mappingfrom inputs to outputs. However, the architecture constrainsthe potential design to that which may be mapped on thearchitecture of an FPGA. Further, a synchronous methodologyis applied, providing time for the signals to settle to a valueabove or below a given threshold, thus ensuring that correct(stable) values are both distributed between components withinthe design and that may be extracted at the outputs.

In algorithmic DNA tiling, on the other hand, such directedpaths may be seen and, rather than physical links, consistof the bonds between neighbouring tiles. As described insection IV, such bonds enable transfer of computation betweenneighbouring tiles. The inputs are integrated into the archi-tecture and thus the paths between input boundary tiles andoutputs are the connections between such boundary tiles andthe outer rule tiles of the DNA tile structure. Although theresulting architecture has similarites to the FPGA architecture— uniform processing tiles, only application specific tiles areincluded in the architecture (for both logical and algorithmicDNA tiling). The constraints that the architecture places onthe design, depend on the DNA tiles that may be created andtheir interconnection. However, as stated, DNA tiling has beenshown to provide universal computation. Thus most designlimitations should be able to be met. Although what might beachieved in practice is still to be investigated. Communicationis purely asynchronous and depends on natural effects and tim-ing of these effects, including bonding time (forward reactionrates) and release time (reverse reaction rates) — for the DNAstrands of the sticky ends, as well as temperature (effects bothtypes of reactions and timing of the overall growing structure).

To ensure that we can achieve a digital design on such aplatform, it is important to ensure that the technology is 100%functional, or at least that the digital abstraction will be achiev-able despite some unreliability in the underlying platform.DNA is essentially an unreliable technology. However recentwork has shown that errors in bonding may be considerablyreduced — see section VII-F.

C. Genotype

To configure a design on a reconfigurable chip, the designis represented in terms of both structure (interconnections) and

functionality (logic). To express both in the genotype wouldinvolve some form of configuration stream (program) for thedevice. Such a configuration stream would result in a lengthygenome, expressed in every individual of the population. Toreduce the length of the genotype, an FPGA may be pre-programmed with respect to the structure, leaving the genotypeto program the logic of the device [16]. A more compactgenotype results, providing the potential for a more effectiveevolutionary process and further less storage requirements tostore the entire population — an important requirement forcomplete hardware evolution. A further approach to ensure amore efficient evolutionary process, is to present an indirectrepresentation in the genotype and apply some form of devel-opmental process during evaluation of each individual [17].Such approaches to reducing the genotype representation ofthe design are all aimed at reducing the scalability challengesinherent in today’s Evolvable Hardware.

To configure a design for DNA tiling technology - asillustrated in section VI, the genotype is dependent on whetherLogical or algorithmic DNA tiling is applied. In AlgorithmDNA tiling, the genotype would represent the seed, boundaryand rule tiles. Evaluation of such a genotype would involvethe natural development of the DNA tile structure undertemperature control. As such, this representation is very muchan indirect mapping, with similarities to rule based repre-sentations being investigated within Evolvable Hardware onFPGA platforms. The quantities of such boundary and ruletiles present, together with the seed tile enable growth of atiling structure through a process of bonding (and release).The resulting structure provides a mapping of the inputs tothe outputs. Thus the genotype representation is input-specific.The required number of tile types to be evolved depends onthe structure of the design i.e. periodic, symmetric circuitsrequire few tile types whereas irregular circuits require agreater number.

In logical DNA tiling, the technology is a soup of super-tiles. To create such a soup, the genotype needs to encode a)the basic tiles of the soup e.g. 1-bit XOR tile or 1-bit ANDtile, and b) the size of the gates sought. Further, the quantityof such tiles to be made available in the soup may either bepre-designed or be evolved and as such, part of the genome.In this case, the tile types to be evolved are dependent on thefunctionality and independent of the structure of the design.During evaluation of such a genome, before fitness can beassessed, the technology needs to form through a process ofbonding to form the super tiles. As such, the representationis perhaps not direct, but also not a developmental process. Itmay be regarded as an indirect representation.

In both genotypes the representation will involve tile de-scriptions. One would expect that such a description wouldencode the sticky ends of the tiles i.e. the DNA sequence of thesticky ends. Often the sticky end lengths are designed in a wayso as to provide some strength in the connection and as such,more challenging designs might involve more varied sticky-end lengths, resulting in longer genotype representations.

D. Fitness Evaluation

Whether one is looking at FPGA technology or DNA tilingtechnology a common fitness goal is to find a functionallycorrect design i.e. a correct mapping from inputs to outputs.

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In FPGA technology, inputs are an external influence tothe architecture of the technology and the implemented design.The synchronous nature of the technology, further ensures thatoutputs at each stage of the design are measurable after astabilising time equivalent to the longest path between oneclocked element and the next. In DNA tiling, on the otherhand, inputs are integrated into the architecture itself duringthe process of self-assembly and the resulting DNA tilingstructure produces the desired outputs without any additionalexternal inputs. Structures may be formed for all combinationsof inputs, in the case of logical DNA tiling, providing outputsthat may be extracted and evaluated. Although DNA tilingis asynchronous, outputs are not readable until the emergingDNA structure(s) have reached equilibrium and outputs areextracted.

Fitness may be extended to evaluate other characteristicsof the design such as area, speed, power and reliability (inreconfigurable technology) or error rate, effect of physical pa-rameters (temperature, concentration of each tile type), amountof total DNA required (cost) and speed/time i.e. how fast theassembly settles down to its final equilibrium.

In the case that fitness evaluation does not take place inreal hardware, as is the case in extrinsic Evolvable Hardwareand DNA tiling, accurate simulators are required. For the caseof FPGA technology, this places a requirement for simulatorswith accurate models of the device physics. More abstractmodels, may be applied in a first phase. However, no realisticevolvable hardware design may be achieved without such a re-alistic simulator in the design loop. Most commonly, variationsof the established spice simulation tools are applied. Similarlyfor DNA tiling suitable realistic simulators are available — asdescribed in section III.

E. scalability

In all three technologies, fitness is the bottleneck of theevolution process. To have a scalable design technique, weneed to ensure that the achievement of complex functionsis achieved with a sub-linear increase in costs i.e. without acorresponding scaling up of resource requirements — designtime, number of physical components and/or computationalresources required [8]. The design time, is of course highlydependent on the fitness evaluation time for an individual inthe process, together with the size of the population and thenumber of generations required to reach the required solution.

Unlike, FPGA technology, programming DNA tiling isinherently an indirect methodology and further, the processfrom the indirect representation to the solution is a naturalprocess of DNA tile bonding and release. Thus the techniquesinvolved are established natural techniques, unlike the case ofdevelopment systems for FPGA technology where researchersaim to find suitable ways to enable structural and/or functionaldesigns to emerge. Thus, DNA tiling has the advantage of anestablished development process. However, such a process is,in nature, error-prone — see section VII-F. Further, such aprocess is relatively slow.

One of the commonly stated strengths within DNA comput-ing is the high parallelism achievable which is also applicableto both forms of DNA tiling. Parallelism is also a strengthof FPGA technology due to its regular structure and potential

for many parallel computations. However, on a much reducedscale. However, in the application of evolutionary techniquesto the design of DNA tiling, can we exploit this parallelismto advantage the design time? Currently, the answer to thisquestion would seem to be no. The reason being that, un-like FPGA technology, there is no available generic parallelarchitecture but rather the architecture and components ofthe technology are designed during the design time and thesolution itself is then tested in practice. As such, the designprocess is extrinsic evolvable hardware. Thus exploitation ofthe parallelism present in nature, is not able to be exploitedduring the design phase. Instead, a sequential simulator isapplied in the evaluation of individuals in the population.

When the number of physical components and /or compu-tational resources is considered, the generality of the FPGAtechnology may be considered a disadvantage as a chip isneeded whether a design fills or partly fills a chip, unless thedesign is a component of a larger design for a chip. However,a smaller chip, suitable for the design may be, of course,considered. In general though, efficient number of gates is aless relevant fitness criteria when FPGAs are the underlyingtechnology and instead issues relevant to area usage such aspower issues are now more relevant.

In algorithmic DNA tiling, similar to FPGA technology,we have a structural design. However scalability would be in-tuitively easier for symmetric rather than asymmetric circuits.However, for logical DNA tiling, symmetry advantages are notpresent — independence of structure, whilst resource usageis advantaged — only the fixed number of tiles required arepresent.

F. Robust Design

A major challenge in electronic design, that evolvablehardware is addressing, is that of robust design/technology.This can be seen as composed of two elements a) a robusttechnology and b) a robust design. Reconfigurable technologiessuch as FPGA technology have to date been consideredas robust technologies, achieved through a rigorous testingprocess during chip production. Such testing is not aimed atdefect free devices, but rather defect free within the constraintsof the digital abstraction model. However, achieving completetesting, even for the digital abstraction limitation, is becomingmore and more of a challenge. This challenge will onlyincrease as technology scales down. Many contributions havebeen made to the achievement of robust evolved designs whicheither tolerate faults or provide some form of adaptive solutionfor detection and correction of faults. Such faults refer tolifetime faults, rather than defects.

As stated, DNA bonding is inherently error-prone and, assuch, any technology that uses DNA will inherit such naturalerrors. In DNA tiling such errors may be seen in erroneous tilebonding. Such errors are significant errors in the technologyand thus an unreliable computation platform. These structuralerrors which thus lead to incorrect pathways from the inputs,may result in erroneous outputs. The flow of informationthrough the assembled structure in algorithmic DNA tiling,provides a cumulative assembly of errors, less present in thelogical DNA tiling approach.

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A number of approaches have been directed at reducingsuch errors [18], [19] and illustrate that DNA tiles may bedesigned so as to enable a drastic reduction in errors, providinga potentially viable platform. As the architecture and the designare highly integrated, such a reduction in errors applies to boththe technology and to the design solution itself.

VIII. DISCUSSION AND FURTHER WORK

When considering some of the important requirementsfor evolvable hardware it is clear that DNA tiling has manychallenges to face. It is an unreliable platform, particularlyalgorithmic DNA tiling with its cumulative errors. However,ongoing work is drastically reducing such errors. Further,due to scaling, FPGA technology may well be an unreliableplatform in the future if yield is to be held. Thus, in both tech-nologies, enabling evolution to create reliable designs, despitesuch errors may be a further challenge to be addressed. Whenconsidering resource usage and thus scalability in terms ofphysical units then logical DNA tiling would seem preferentialto either algorithmic DNA tiling or FPGAs. However, whenconsidering evolutionary time, algorithmic DNA tiling may beadvantaged, assuming the search for an exact number of tilesrequired for a specific design creates a more complex search.

Investigations are needed to consider evolution of simpledigital circuits in both algorithmic and logical DNA tilingand in particular, comparison thereof. Although simulators areavailable, ways to efficiently conduct such extrinsic experi-ments should be investigated. Further, acceptance of viabilityof the results requires wet-lab experimentation of the evolvedsolutions.

It may be concluded that both logical and algorithmic DNAtiling, provide interesting potential technologies for furtherinvestigation. Ongoing work (of the authors) is looking atways to further reduce the cumulative errors whilst avoidingany decrease in growth time of the assembly. Further, waysto introduce adaptivity are under investigation. In addition,initial experiments are being run in both simulation and wet-lab environments.

REFERENCES

[1] A. Thompson, “An evolved circuit, intrinsic in silicon, entwined withphysics,” in 1st Int. Conf. on Evolvable Systems 1996, Springer Verlag,1996, pp. 390–405.

[2] A. Stoica, “Evolution of analog circuits on field programmable transistorarrays,” in Proceedings of NASA/Dod Workshop on Evolvable Hardware(EH2000), 2000, pp. 99–108.

[3] A. M. Tyrrell, E. Sanchez, D. Floreano, G. Tempesti, D. Mange,J. Moreno, J. Rosenberg, and A. Villa, “POEtic tissue: An integratedarchitecture for bio-inspired hardware?” in Proceedings of 5th Interna-tional Conference on Evolvable Systems, 2003, pp. 129–140.

[4] S. Harding and J. F. Miller, “Evolution in materio: Evolving logic gatesin liquid crystal,” in Proc. Eur. Conf. Artif. Life (ECAL 2005),Workshopon Unconventional Computing: From cellular automata to wetware,2005, pp. 133–149.

[5] E. Winfree, “Algorithmic self-assembly of DNA,” Ph.D. dissertation,California Institute of Technology, 1998.

[6] H. Yan, F. Liping, T. H. LaBean, and J. H. Reif, “Parallel molecularcomputations of pairwise exclusive-or (XOR) using DNA string tileself-assembly,” Journal of the American Chemical Society, vol. 125,pp. 14 246–14 247, 2003.

[7] A. Carbone and N. C. Seeman, “Circuits and programmable self-assembling DNA structures,” Natl. Acad. Sci. USA, vol. 99, pp. 12 577–12 582, 2002.

[8] P. C. Haddow and A. M. Tyrrill, “Challenges of evolvable hardware:Past, present and the path to a promising future,” Journal of GeneticProgramming and Evolvable Machines, vol. 12, no. 3, pp. 183–215,2011.

[9] H. Wang, “Proving theorems by pattern recognition ii,” Bell Syst. Tech.J, vol. 40, pp. 1–42, 1961.

[10] T. J. Fu and N. C. Seeman, “DNA double-crossover molecules,”Biochemistry, vol. 32, pp. 3211–3220, 1993.

[11] P. Yin, B. Guo, C. Belmore, W. Palmeri, E. Winfree, T. H. LaBean,and J. Reif, “TileSoft: Sequence optimization software for designingdna secondary structures,” 2004.

[12] P. W. K. Rothemund, “A DNA and restriction enzyme implementationof turing machines,” in Dimacs series in discrete mathematics andtheoretical computer science, 1996, pp. 75–119.

[13] P. W. K. Rothemund, N. Papadakis, and E. Winfree, “Algorithmic self-assembly of DNA sierpinski triangles,” PLoS Biology, vol. 2, no. e424,2004.

[14] C. Mao, T. H. LaBean, J. H. Reif, and N. C. Seeman, “Logicalcomputation using algorithmic self-assembly of DNA triple-crossovermolecules,” Nature, vol. 407, pp. 493–496, 2000.

[15] P. C. Haddow, G. Tufte, and P. van Remortel, “Shrinking the geno-type: L-systems for EHW,” in International Conference on EvolvableSystems: from Biology to Hardware, 2001, pp. 128–139.

[16] P. C. Haddow and P. van Remortel, “From here to there: Future robustEHW technologies for large digital designs,” in ICES-2001, 2001, pp.232–239.

[17] T. Gordon and P. J. Bentley, “Towards development in evolvablehardware,” in Proceedings of the NASA/DoD Conference on EvolvableHardware, 2002, pp. 241–250.

[18] E. Winfree and R. Bekbolatov, “Proofreading tile sets: Error correctionfor algorithmic self-assembly,” in DNA Based Computers 9. Springer-Verlag, 2004, pp. 1980–1981.

[19] H. L. Chen and A. Goel, “Error free self-assembly using error pronetiles,” in DNA Based Computers 10. Springer-Verlag, 2005, pp. 62–75.

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