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Minimising the Hardware Resources for aCellular Automaton with Moving Creatures

FB InformatikFG RechnerarchitekturMathias HalbachRolf Hoffmann

ContentIntroductionDescription of the problemMethodologyImplementation VariantsConclusion

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Creatures and the Environment

Challenge:Find the best behaviour of moving creatures automatically.Question in detail:n creatures are moving around in an unknownenvironment in order to visit all cells in shortest timewithout map generation.

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Modelling

based on the cellular automata model by John von Neumann

– massively parallel– perfectly suited to be supported by hardware

fixed obstacles, empty cells, moving creatures.each creature (max. one per cell)

– can observe and move only in one direction (front cell),– can only move to empty cells,– must turn left or right,– has a state s (= creature's memory)

and an algorithm (= rule). ?

move and turn turn only

blockedfree

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Problem Description

environment– obstacle h

location– creature c or ci

– position pi

– position of front cellcreature's

– state si

– direction ri

signals– turn di

– moving condition mi= can be visited

next position

next state and direction

ipr

ipr

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Methodology of Evaluation

generate state machine (behaviour)

discard similar state machines

∀ environments: simulate and evaluate

discard bad behaviour

store performance of state machine for later statistics

∀al

gorit

hms

FPG

A H

ardw

are

Sof

twar

e

identify best algorithms

detailed statistics (state machines, environments)

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Amount of State Machines

inspected different n state algorithms– n = 5: (2 × 5)(2 × 5) = 1010 = 10,000,000,000– n = 6: (2 × 6)(2 × 6) = 1212 = 8,916,100,448,256– n = 7: (2 × 7)(2 × 7) = 1414 = 11,112,006,825,558,016

very time consuming

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One of the Best 6-State Algorithm

1 L3 Lm2 L 1 Rm0 L5 Lm4 R0 Rm5 R4 Lm3 R2 Rm

0 00 11 01 12 02 13 03 14 04 15 05 1

s r

v

m

Lm

L

R

Rm

0 2

1

3 5

4

L

L

R R

LmLmRmRm

Lm

L

R

Rm

0 2

1

3 5

4

L

L

R R

LmLmRmRm

s : control stater : directionv : new directionm : creature can moveL/R : turn left/R if (m=1)Lm/Rm : turn left/R and move if (m=0)

d

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Performance of Different Algorithms

top 10 results for one environment, 6 states

What about multiple creatures?

<

generations

cros

sed

cells

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Problem: Collision

multiple creatures want to move to the same empty cellone solution

– no priority– forbidden for all

our implementation– front cell collects requests– evaluates (Σ > 1?)– sending collision warning (occupied) or grant signal– can be done within the current clock cycle

front cell

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Other Kind of Implementation

pipeline structure– phase 1: forecast for collision based on position– phase 2: calculate next state, position, and direction– forwarding needed!– forwarding results in single-cycle implementation– i. e. no pipelining possible

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Implementation Variant: Uniform

union of environment cell and creature cellmassive parallel algorithm

– if creature is blocked: state and direction is set to new values;– if creature can move: empty cell becomes creature with new

direction and state, meanwhile creature becomes empty cell;– all other empty cells and obstacles remain unchanged.

collision detection– for empty cell which is front cell of multiple creatures:

send occupied signal and remain empty;– for creature: if front cell sends occupied, do blocked action.

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Implementation Variant: Separated

creatures (state machines) anchored on fixed placeconnection to area via position pointer (i.e. multiplexer)creature stores

– position pi

– state si

– direction ri

collision detection by extra logic

ipr

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Implementation Variant: Augmented A

intelligent environment (iEnv.) similar to "uniform"creatures functions separated from environmentenvironment stores creature index ci and direction rcreature is state machine

– input from area: movable mi

– output to area: turn di

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Implementation Variant: Augmented B

intelligent creature (iCrea.) similar to "separated"environment cells know about

– own index (position) 0, 1, 2, …– occupied by creature i pi

– direction to front cell ri

– the calculated multiple access status of the front cell mi

multiplexer and collision detection are shifted into the area cells

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Chip Overview for 8 × 8 Field with 8 Creatures

FPGA Altera Cyclone EP1C20F324C7

– clock at 50 MHz– change algorithm (rule)

during runtime– generate statistics– showing sequence of

calculationserial interface

– connected to a PC– for control and to archive data

easily

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Experiment Result (Fit to 50 MHz)

5,433 LE 56 MHz

11,766 LE 51 MHznot possible

20,007 LEdoesn't fit

17 × 16 (2 creatures)

4,846 LE 55 MHz

11,088 LE 52 MHz

3,159 LE 53 MHz

18,883 LE doesn't fit

16 × 16 (2 creatures)

2,988 LE 51 MHz

6,346 LE 51 MHz

2,515 LE 54 MHz

11,582 LE67 MHz

12 × 12 (2 creatures)

5,674 LE 64 MHz

6,727 LE 39 MHz

3,785 LE 50 MHz

7,687 LE 76 MHz

8 × 8 (8 creatures)

1,873 LE 56 MHz

3,295 LE 52 MHz

1,623 LE 60 MHz

5,414 LE 81 MHz

8 × 8 (2 creatures)

1,439 LE 61 MHz

3,181 LE 56 MHz

1,312 LE 65 MHz

4,761 LE 52 MHz

8 × 8 (1 creature)

augmented B (iCrea.)

augmented A (iEnv.)

separateduniformenvironment

LE = logic elements

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Analysis

Uniform: restricted to small field sizeSeparated: reasonable for small amount of creatures,

but limited field size (256 positions)Augmented A (iEnv.): restricted to small field sizeAugmented B (iCrea.): reasonable for large fields or many creatures

2 creatures8 × 8 cells

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Conclusion

To find an optimization of a creature's state machine needs a lot of computation time.The logic should be minimized in order to increase the degree of parallelism and speeding up the optimization.Different implementation variants have been proposed and evaluated.

It is better to separate the functionality of the cells than to integrate them together.

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Thank You for Your Attention!

Mathias Halbachhalbach@informatik.tu-darmstadt.deTU Darmstadt, Computer Architecture GroupHochschulstrasse 1064289 Darmstadt, Germany

℡ +49 6151 16 3713+49 6151 16 5410http://www.ra.informatik.tu-darmstadt.de/

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Field Size 4 × 4 (relative more creatures)

0

1000

2000

3000

4000

5000

6000

1 2 4 8 12 16

Creatures

Logi

c El

emen

ts augmented B

augmented A

separated

uniform