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Arithmetic Operations on Self-Replicating Cellular Automata

Arithmetic Operations on Self-Replicating Cellular Automata. Enrico Petraglio Logic Systems Laboratory. Summary. Motivations Introduction to the CA Theoretical Notions Binary Addition Binary Multiplication Implementation on the CA Conclusions. Motivations.

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Arithmetic Operations on Self-Replicating Cellular Automata

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  1. Arithmetic Operations on Self-Replicating Cellular Automata Enrico Petraglio Logic Systems Laboratory

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

  3. Motivations • Von Neumann’s Universal Constructor: • Universal Construction • Universal Computation Is useful computation with self-replicating automata necessarily associated with high complexity?

  4. Self-Replication

  5. Processor Cell Result Computation Left Data Cell Right Data Cell 1-bit Addition Steiglitz, Squier, Jakubow (1994)

  6. Processor Cell Left Addend Right Addend N-bit Binary Addition Steiglitz, Squier, Jakubow (1994)

  7. First Collision Left Multiplicand Right Multiplicand 3x3 Binary Multiplication Steiglitz, Squier, Jakubow (1994)

  8. Data cell + carry 3x3 Binary Multiplication Steiglitz, Squier, Jakubow (1994)

  9. 0 0 1 1 3x3 Binary Multiplication Steiglitz, Squier, Jakubow (1994)

  10. Collision Rules 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 0 Before After Before After

  11. Implementation on Self-Replicating Loops • Addition of four • 7-bit numbers • (13+16+10+37+19)

  12. Addition + Multiplication (1+1+4) x (2+2 +3)

  13. 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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