An Overview of Evolutionary Cellular Automata Computation

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An Overview of Evolutionary Cellular Automata
Computation

• Scott McQuade
• January 24, 2008

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A2 Papers

• J.P.Crutchfield and M.Mitchell. The evolution of
  emergent computation. PNAS, 92 (23) 10742, 1995.
  
• M.Mitchell, J.P.Crutchfield and R.Das. Evolving
  cellular automata to perform computations. In T.
  Back, D. Fogel, and Z. Michalewicz (editors),
  Handbook of Evolutionary Computation. Oxford
  Oxford University Press, 1998.

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Outline

• Objectives
• Methodology
• Results
• Interpretation of Results

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Objectives

• Study the evolution and emergence of spatially
  extended, decentralized computing
• Occurs naturally (insect nests, aggregation of
  slime mold, parallel processing by sensory
  neurons, economical markets/pricing) (Crutchfield
  and Mitchell, 1995)
• Applications to computations systems
• Parallel Processing
• Lack of Central Processor
• More Efficient Communications

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One-Dimensional Cellular Automata (Mitchell,
Crutchfield, and Das, 1998)
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Example Results (Mitchell, Crutchfield, and Das,
1998)
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The Task

• Density Classification
• If the initial configuration contains more 1s
  than 0s, all cells should eventually switch to
  1s
• If the initial configuration contains more 0s
  than 1s, all cells should eventually switch to
  0s
• This is referred to as the ?c(1/2) Task
• ?0 refers to the density of 1s in the initial
  configuration

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The Task

• No Cellular Automata can perform the ?c(1/2)
  task perfectly across for all N
• Even for fixed N, a single cell, or a linear
  combination of cells, does not have the
  computation power to perform the ?c(1/2) task
  well

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Task Parameters

• N 149
• r 3
• 27 128 bit rule string 2128 possible rules
• ?0 was uniformly distributed between 0 and 1 for
  the test cases
• NOT the unbiased distribution as it was too
  difficult
• Maximum Time of 2N to produce the correct
  behavior

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Basics of Genetic Algorithms

• Initial pool of algorithms or strategies
• Run all algorithms Obtain results
• Fitness Function to evaluate the results of
  each existing algorithm
• Reproduction using the top performing algorithms
  recombination (crossover) and mutation
• Repeat for multiple generations

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GA Parameters

• The rules of the automaton will evolve, not the
  board itself
• 100 initial random rules (generated with some
  initial biases)
• Each rule evaluated on 100 uniformly distributed
  initial configurations (per generation)
• Fitness was the fraction of the 100 where correct
  behavior was produced
• For each generation
• Top 20 rules were retained
• Crossover of random pairings of the top 20 rules
  to produce the new 80 rules
• 2 random mutations per crossover
• 100 Generations

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Results of Selected Rules (Crutchfield and
Mitchell, 1995)
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Block Expanding Rules (Mitchell, Crutchfield, and
Das, 1998)
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Block Expanding Rules

• Simpler Strategy
• Works well with small or large ?0
• Does not exhibit coordinated communication flow
  processing done locally
• Does not scale well

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Particle Based Rules (Mitchell, Crutchfield, and
Das, 1998)
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Particle Based Rules

• Complex patterns evolve
• Each pattern region (domain) can be classified
  and recognized be a DFA
• The constant patterns can be filtered out,
  leaving only the boundaries between domains
• These domain boundaries act like particles,
  travelling at constant velocities and interacting
  with each other

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Particle Based Rules (Crutchfield and Mitchell,
1995)
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Particle Based Rules(Crutchfield and Mitchell,
1995)
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Synchronization Task (Mitchell, Crutchfield, and
Das, 1998)
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Conclusions

• Complex particle-based rules evolved infrequently
  but consistently (7 out of 300 runs)
• The evolution consisted of distinct epochs with
  distinct innovations

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Conclusions

• Using an unbiased initial configuration (?0 ½),
  was too difficult for initial generations
• A uniform 0, 1 ?0 distribution was used, but
  this proved to be too easy in later generations
• The authors mentioned the possibility of a
  co-evolution sheme
• Breaking of symmetries proved to be a problem

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Conclusions

• Possible applications to more complex real-world
  problems (image processing)
• Insight into natural evolutionary behavior

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References

• 1. J.P.Crutchfield and M.Mitchell. The evolution
  of emergent computation. PNAS, 92 (23) 10742,
  1995.
• 2. M.Mitchell, J.P.Crutchfield and R.Das.
  Evolving cellular automata to perform
  computations. In T. Back, D. Fogel, and Z.
  Michalewicz (editors), Handbook of Evolutionary
  Computation. Oxford Oxford University Press,
  1998.