Arithmetic Operations on SelfReplicating Cellular Automata

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Arithmetic Operations on Self-Replicating
Cellular Automata

• Enrico Petraglio
• Logic Systems Laboratory

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Summary

• Motivations
• Introduction to the CA
• Theoretical Notions
• Binary Addition
• Binary Multiplication
• Implementation on the CA
• Conclusions

3
Motivations

• Von Neumanns Universal Constructor
• Universal Construction
• Universal Computation
• Is useful computation with self-replicating
  automata necessarily associated with high
  complexity?

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Self-Replication
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1-bit Addition
Steiglitz, Squier, Jakubow (1994)
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N-bit Binary Addition
Steiglitz, Squier, Jakubow (1994)
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3x3 Binary Multiplication
Steiglitz, Squier, Jakubow (1994)
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3x3 Binary Multiplication
Steiglitz, Squier, Jakubow (1994)
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3x3 Binary Multiplication
Steiglitz, Squier, Jakubow (1994)
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Collision Rules
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
Before After
Before After
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Implementation on Self-Replicating Loops

• Addition of four
• 7-bit numbers
• (1316103719)

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Addition Multiplication
(114) x (22 3)
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Conclusions

• Too complex!!!
• Self-replication not really necessary
• Useful computation with self-replicating automata
  IS feasible
• This approach will be useful for the development
  of self-replicating hardware

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