/

IMPLEMENTATION OF CELLULAR LEARNING AUTOMATA ON

RECONFIGURABLE COMPUTING SYSTEMS

Morteza Saheb Zamani and Farhad Mehdipour and Mohammad Reza MeybodiComputer Engineering DepartmentAmirkabir University of Technology

{szamani, mehdipur, meybodi} @ce.aut.ac.ir

AbstractReconfigurable computing systems (RCS) use the

flexibility of programmable devices and the speed ofhardware to implement high performance systems.Implementation of RCS is normally made by means ofprogrammable devices, such as FPGAs. On the otherhand, recently, cellular learning automata (CLA) havebeen proposed as a combination of conventional cellularautomaton and learning automaton. Software simulationof CLA has shown it to be successfulfor solvingsomehard problems. However, the process on conventionalcomputers is slow. To overcome this problem, weimplemented CLA in hardware. In addition, for someapplications which necessitate run time changes forparameters, the ability of run-time reconfiguration (RTR)in hardware is a solution. In this paper, the design andimplementation of CLA on a reconfigurable system arepresented. Experimental results show considerable speed-up gain of RCS version over the software version.Independence on CLA dimensions is another benefit ofreconfigurable hardware implementation of CLA. Inother words, by increasing the dimensions of CLA, thetime neededfor running reconfigurable CLA implementedon hardware remains constant.

Keywords: Reconfigurable systems, Cellular learningautomata, Hardware accelerator.

1. Introduction

Cellular automaton(CA) was introduced as a model foranalyzing complicated systems behavior [1] [13] [14]. Itconsists of a regular set of cells each of which has several

CCECE 2003 -CCGEI 2003, Montreal, May/mai 20030-7803-7781-8/03/$17 .00 ~ 2003 IEEE

values. On the other hand, learning automaton(LA),introduced in early 1960 can update its actions in astochastic environment for improving its performance.Each LA uses a learning algorithm and learns how tointeract best with the environment. The model of cellularlearning automaton (CLA) has been proposed as acombination of cellular and learning automata. CLAcontains several number of cells. In each cell, an internallearning automaton determines the status or action of thecell. CLA has been used in some applications such ascommerce network modeling and image processing[8] [4][9].

The rest of the paper is organized as follows: section 2,3 and 4 briefly explains the cellular automata, learningautomata and cellular learning automata, respectively. Anoise elimination approach based on cellular learningautomata are presented in section 5. Finally in section 6, areconfigurable hardware version of CLA for noiseelimination and experimental results are presented.

2. Cellular Automata

Cellular automata (CA) are mathematical models forsystems consisting of a large number of simple identicalcomponents with local interactions. The simplecomponents act together to produce complicated patternsof behavior. CA can perform complex computations withhigh degree of efficiency and robustness. In addition, theycan be used to model the behavior of complex systems inthe nature.

It is called cellular, because it is made up of cells likepoints in a lattice or like squares in a checker board and itis called automaton, because it follows a simple digitalrule. There are two problems concerning CA: forwardproblem and inverse problem. In the forward problem, thegoal is to determine (predict) properties of a given CArule and in the inverse problem, a description of some

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properties is given and the goal is to find a rule or a set ofrules with these properties.

A CA consists of a fmite dimensional lattice of siteswhose values (internal states) are restricted to a finite setof integers rp =(O,J, k-I). The value of each site at anytime instant, n, is a function of the values of theneighboring sites at the previous time instant, n-J. Basedon the nature of this function, CAs are classified in twomain groups, namely deterministic CAs and stochasticCAs. Given a finite set rp and an integer d, one canconsider a d-dimensional lattice 7! in which every pointhas a label tTom the set rp. Each site, u, in the d-dimensional lattice 7! is represented by a d-tuple (Z"Z2...,z,J. In the deterministic cellular automata (DCA), thevalue of each site at any time instant, n, is determined bya deterministic mapping of the values of the neighboringsites at the previous time instant, n-J. In stochasticcellular automata(SCA), this mapping is stochastic.[1][10] [14]

3. Learning Automata

Learning automata(LA) is an abstract model, whichperforms certain actions. A probabilistic environmentevaluates the action performed by LA and provides anappropriate response for it. LA uses this response andprepares the next reasonable action. Figure I shows therelationship between the environment and LA. In a LA ,the environmentE is definedas a triple, E={a.p.cJwherea={al,a:z,...,a,}is the input set, P={PI,P2,...,Pm}is the output

set and c=(Q,c2,''',c,}is the set of penalty probabilities.When fJ has two members, PI=I is considered as

penalty and h =0 is considered as reward. Cj is a

probability of unfavorable result of action aj. Theenvironment of LA classified into stationary and v"riabls:

structure. In a stationary environment, Cj values do not

change during the learning process which in a variableenvironment, they can change[5] [6] [7] [I I].

4. Cellular Learning Automaton

Recently, Cellular learning automata(CLA) has beenintroduced as a combination of conventional learning andcellular automaton[12][8]. CLA is a model for systemsconsisting of simple elements. In this model, the behaviorof each element is modified based on its experience andthe behavior of neighboring cells. CLA has a regularstructure of cells, containing one or more LAs. As inCAs, a local rule determines reward or penalty forperforming an action.

The purpose of reward or penalty of the cells issynchronous updating of CLA to reach a certain goal.

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CLA is defined as < L,v,Q,n,et>> in which L = {/)'/2,...,/n}

is the set of cells in a Cartesian network. Q={QI,Q2,...,Qk}is

the set of actions belonging to a cell in an automaton.n ={x:L~ QJ=QN is the state space and et>is a rule used inthe CLA. V ={Vi,je L} is a set of cells in theneighborhood of a cell i if it has the two followingproperties:

a)i~v. VieL,b) iev. ifT jevj Vi,jeLTwo 'common kinds of neighborhood are von

Neumann and Moor(see Figure 2). The CLA shown inFigure 3 represents the general functionality of a CLA. Ina CLA, Each cell first chooses one of the actions tTomtheactions set. This action is selected randomly or based onthe previous experience. The reward or penalty is given inresponse to this action selection, and then, the internalautomaton of the cell is updated. Updating all of theautomata is performed synchronously. After updating,each automaton chooses another action. The process ofaction selection and rewarding or penalizing continuesuntil the CLA become stable or certain criteria are met.The CLA shown in Figure 3, uses von Neumannneighborhood. The happy cells have received reward andthe sad ones, have been penalized in the previous stage.

a(n)Random Environment

Learning AutomatalI(n)

Figure 1. Relationship between LAandenvironment

Neighborhood Von Neumann Moor neighborhood

Figure 2. Two kinds of neighborhood

5. Application of CLA to the Elimination ofNoise in Images

CLA has been used to solve some hard problems suchas image processing problems[4]. In this paper, theapplication of CLA to the elimination of noise in binary(black and white) images is represented. Both hardwareand software implementations were investigated. Resultsshow considerable speedup of hardware implementationas compared with software implementation. We usedstationary structure learning automata (L2N.2) with two

actions. Each cell performs two actions for black pixelsand white pixels in the image. The rule used for CA ismajority rule. According to this rule, if the number ofneighbors of a cell and the cell itself performing anidentical action, is greater than a threshold value (e.g. halfof the number of cells in neighborhood), then this cellwill be rewarded; otherwise it will be penalized. Someparameters, such as the neighborhood type and thresholdvalue, can be changed during the learning process. Thefinal status of the cells in the CLA represents the color ofrespective pixels in the image.

In the hardware implementation, an optimized versionof a stationary environment and a majority rule-based CAwere implemented. The optimization was accomplishedfor area as the primary objective and the performance asthe secondary objective.

CLA

Figure 3. Cellular Learning Automaton

6. The ReconfigurableHardware Versionand the Experimental Results

Reconfigurable computing systems (RCS) use theflexibility of programmable devices and the speed ofhardware to implement high performance systems.Applications with inherent parallelism; local connectionsbetween components, integer arithmetic computations andsimple decisions are appropriate for implementation onRCS and CLA is one of these applications [3][2].

On the other hand, CLA has been successful in imageprocessing problems. In addition, for some applications,there are parameters concerning cellular or learningautomata, which necessitate run time changes in thehardware architecture. In such cases, the ability of run-time reconfiguration (RTR) is a solution.

RCSs are normally implemented in programmabledevices, such as FPGAs(Field Programmable GateArrays). To be able to change the configuration of thedevice during its operation, RAM-based FPGAs must beused.

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A modified algorithm of noise reduction in black andwhite images uses variable threshold value and variantneighborhood of cells during learning process of CLA.We used a hardware reconfigurable version for theimplementation of this kind of CLA. In thisimplementation, some configurations were provided asbefore they are used during learning process of CLA.Optimized versions of configurations for loading onFPGA were generated.

One of the problems in the hardware implementationof a CLA on an RCS is the large number of I/O pinrequired for representing each status of CLA cells. This is, each cell should have one output, to show that thecorresponding pixel is white or black. The CLA we usedfor noise elimination had at least 128x128 cells in a twodimensional array. Therefore, the number of CLA outputsexceeded the number of available I/O pins ofconventional FPGA devices. We designed the CLA cellsin such a way that the outputs are saved in internal bitsand the outputs are needed to be observed, a shiftingprocess is performed by setting the observe input ofcell(Figure 4). By clocking the CLA when observe inputis enable, the output of the cells will be observable. Foran NxN CLA, N clock periods are required to observe alloutputs. This approach increases area overhead of thedesign but reduces the required I/O pins.

The algorithm was implemented on VIRTEX tromXilinx.The running time was measured for software andhardware implementations. First, we added at most 30percent noise to images. Then we used the reconfigurableversion of 128x128 CLA for the elimination of this noise.Experiments showed that the hardware version hadconsiderable speedup(at least 3000 times) compared tosoftware implementation(see Table 1). Another importantadvantage of reconfigurable hardware CLA is that due tothe inherent parallelism of CLA, increasing thedimensions of CLA does not change the time needed forrunning it. In the other words, the running time isindependent of the size of CLA. Figure 5 shows the noisereduction trom the image which has the noise.

Table 1. Software and Hardwarerunning time--- -- - --

Image Software running Hardwarerunning speedupNo. time(sec) time(Jlsec)

1 0.8 210 38092 0.75 196 38263 0.87 210 41424 0.8 182 43955 0.06 14 42856 0.74 154 48057 0.13 42 3095

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[3] S. Hauck, A. Agrawal, "Software Technologies forReconfigurable Systems", Northwestern UniversityDepartment Of Electrical and Computer Engineering.Technical report, 1996.

[4] Kharazmi, M. R. and Meybodi. M. R., "Application ofCellular Learning Automata to Image Segmentation",Proceeding of Tenth Conference on Electrical Engineering(IO'h ICEE), University of Tabriz, V01. I, pp. 298-306,2001.

[5] Lakshmivarahan, S., "Learning Algorithms: Theory andApplications", New York, Springer Verlag, 1981.

[6] Mars, P., Chen, J.R. and Nambir, R., "Learning Algorithms:Theory and Applications in Signal Processing, Control andCommunications", CRC Press, Inc., pp. 5-24, 1996.

[7] Meybodi, M.R. and Lakshmivarahan, S., "& - Optimalityof a General Class of Absorbing Barrier LearningAlgorithms", Information Sciences, Vol. 28, pp. 1-20, 1982.

[8] Meybodi. M. R. and Beygi, H.Taherkhani, M.," CellularLearning Automata", Proceedings of 6th Annual CSI

otlselYeD

Computer Conference, Computer Engineering Department,Cniversity ofIsfahan, pp. 153-156,20-22 Feb 2001.

[9] ~Ieybodi, M. R. and Khojasteh, M. R., "Cellular LearningAutomata as a Model for Commerce Networks",Proceedings of 6th Annual CSI Computer Conference, CEDepartment, University of Isfahan, pp. 284 -295, 20-22 Feb.200 I.

[10] Mitchell, M., "Computation in Cellular Automata: ASelected Review", Technical Report, Santa Fe Institute,Santa Fe, U.SA, 1996.

[11] Narendra, K.S. and Thathachar, MAL., "LearningAutomata: An Introduction", Prentice Hall, Inc., 1989.

[12] Taherkhani, M., "Proposing and Studying of CellularLearning Automata as a Tool for Modeling Systems", M.Sc.Thesis, Computer Eng. Dept., Amirkabir University ofTechnology, Tehran, Iran, 2000.

[13] Toffoli, T. and Margolus, N., "Cellular AutomataMachines", the MIT Press, 1987.

[14] Wolftam, S., "Statistical Mechanics of Cellular Automata",Review of Modem Physics, 55, pp. 601-644, 1983.

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Figure 4. An implemented Cell of CLA

Figure 5.00 ~ ~

Elimination of noise in Black &White image (a) primary image (b)noisy image (c) noiseeliminated image

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