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From Asynchronous Cellular Automata to Nanocomputers

From Asynchronous Cellular Automata to Nanocomputers. Ferdinand Peper. National Institute of Information and Communications Technology (NICT), Nano ICT Group, Kobe, Japan University of Hyogo, Division of Computer Engineering, Himeji, Japan.

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From Asynchronous Cellular Automata to Nanocomputers

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  1. From Asynchronous Cellular Automata to Nanocomputers Ferdinand Peper • National Institute of Information and Communications Technology (NICT), • Nano ICT Group, Kobe, Japan • University of Hyogo, Division of Computer Engineering, Himeji, Japan * Communications Research Laboratory (CRL), Nanotechnology Group + Himeji Institute of Technology, Dept. of Electrical Engineering

  2. Diam. Hair Holes in coffee filter Bacte-rium Virus Protein Atom Sand Diam. DNA Down to Nanometers 1mm 1μm 0.1μm 0.01μm 0.1mm 0.01mm 1nm 0.1nm Automata '06

  3. Moore’s Law # of transistors on chip doubles every 18 months Combination of increases in transistor densities and increases in chip sizes History: (1965) Doubling every 12 months (1975) Doubling every 24 months (1980’s) Doubling every 18 months Factors change: devices, design, architectures Automata '06

  4. Von Neumann Architecture • Program stored in memory like data (Neumann, etc.; 1949) CPU Memory Automata '06

  5. Von Neumann Architecture • Bottleneck between CPU and Memory → Wiring not local ‒ much chip area for wiring • Irregular structure → Design manpower required 3 year design staff Million Transistors → Complicates manufacturing Increasingly Problematic as Integration Density Rises Automata '06

  6. Top-down Manufacturing • Uses a Master Scheme • Any structure possible (irregular) • Lower limit to feature sizes Automata '06

  7. Bottom-up Manufacturing Self-Assembly Directed Self-Assembly Molecular Self-Organization Molecular Pattern Matching Styreneline [Wolkow, 2000] DNA Tiles [Yan et al., 2003] (Semi-) regular structures Regular / random structures Basically dumb materials Some functionality Automata '06

  8. Configuration needed Configuration may include defect-tolerance Easier to make Harder to use Configuration needed Defect-tolerance separate issue May be harder to make Easier to use Random and Regular Structure Regular structure Random structure Cellular Automata Neural Networks, Swarms Automata '06

  9. Computer Architectures: Timing • Acceptance of synchronous timing (early 1950’s) Problems: → Only ~1% of transistors used simultaneously, but all draw power ⇒ Heat dissipation ! → Wire delays become increasingly important Clock does not scale with integration Should we go back to asynchronous timing? Automata '06

  10. Ouch! Heat Dissipation Asynchronous timing: • Clocking on nanometer scales difficult • Heat dissipation at high integration densities Advantages of Asynchronous Circuits become clearer with higher integration densities Automata '06

  11. Asynchronous Cellular Automata Automata '06

  12. Synchronous Cellular Automaton Update All Cells at the Same Time Automata '06

  13. Cells are randomly selected to be updated Every cell gets timer counting 0→1→2→0... Every cell remembers previous and current state If cell is 1 step ahead of any neighbor, it will not be updated, even when selected O(3n2) states [Nakamura,74] O(n2+2n) states [Lee,04] Simulating SCA on ACA From: [Lee et al.,04] Automata '06

  14. Simulation on Asynchronous Cellular Automaton (ACA) Update Each Cell at Random Times Automata '06

  15. Which CA are Useful for Nanocomputing? • Direct asynchronous implementations in which only cells near signals are active • Low complexity of cells • Few states • Few transition rules (no central rule table) Automata '06

  16. Timing in ACA A CA is restricted asynchronous if at each time step at most one cell that is randomly selected from the cell space undergoes a state transition A CA is completely (or purely) asynchronous if at each time step each cell in the cell space has a certain probability p (0 < p < 1) to undergo a state transition, which is independent of the other cells Automata '06

  17. Signal Transmission on Asynchronous CA Transition rules applied with certain probability when Left-Hand-Side matches pattern in cell space Automata '06

  18. Design Principles of ACA (1) • Serialize transitions critically dependent on update ordering • Sheath of signal cannot advance first; otherwise mess • Controlled advance of kernel: Advance of temporary kernel state Advance of sheath along it Permanent advance of kernel Automata '06

  19. Design Principles of ACA (2) • Temporal blocking of a cell’s update until its neighborhood • matches Left-Hand-Side of a transition rule • Upon advance of kernel, advance of tail is unblocked • Rear / side of tail cleared after center part • of tail has advanced Order of clearing unimportant Automata '06

  20. Update due to rule necessary for other situation Reverse rule Nondeterminism Design Principles of ACA (3) • Reverse rules for deadlock situations (backtracking) Note: Rules are applied with probability p < 1 Deadlock This is impossible for synchronous cellular automata Automata '06

  21. Signal Transmission on Asynchronous CA Transition rules applied with certain probability when Left-Hand-Side matches pattern in cell space 6 4 4 6 1 1 2 3 4 5 1 1 6 6 4 4 Semi-totalistic asynchronous CA with 3 states, Moore neighborhood and 6 transition rules [Adachi et al., 2004] Automata '06

  22. c c 1 Rule 1: 1 6 Chimp signal – Rule 1 Automata '06

  23. c c 4 Rule 2: 1 3 Chimp signal – Rule 2 Automata '06

  24. c c 7 Rule 3: 1 0 Chimp signal – Rule 3 Automata '06

  25. c c 3 Rule 4: 0 5 Chimp signal – Rule 4 Automata '06

  26. c c 4 Rule 5: 1 3 Chimp signal – Rule 5 Automata '06

  27. c c 1 Rule 6: 1 6 Chimp signal – Rule 6 Automata '06

  28. c c c c c c c c c c 4 7 4 3 1 Rule 2: Rule 5: Rule 6: Rule 4: Rule 3: 1 0 1 1 1 3 6 3 5 0 c c 1 Rule 1: 1 6 Chimp Signal - Rules Automata '06

  29. 5 2 4 4 4, 1 4 4 c c 1 1 6 Rule 1: c c 1 1 Rule 6: 6 c c 3 4 1 Rule 2: 5 2 c c 3 4 1 Rule 5: c c 7 1 0 Rule 3: c c 5 3 0 Rule 4: Transmitting sequence of signals Automata '06

  30. Crossing Signals • Signals negotiate with each other for passage (arbitration) • Arbitration possible due to asynchronous updating Automata '06

  31. Map Circuit onto CA Computation on Asynchronous Cellular Automata Computation Problem Convert Problem into Circuit Cellular Automaton (CA) Robust to signal delays in lines or components Automata '06

  32. Nanocomputer Operations Alternative operational principles: • Signal propagation and interaction by different mechanisms like molecular interactions (e.g. Token-Based) Automata '06

  33. What is a Token? • Abstract unit of information used for passing a message between devices How to Represent it? • Indivisible discrete unit • Numbers of tokens change only as result of operations Automata '06

  34. Signals are Tokens Particles Cascades Ballistic signals Interaction-based signals Automata '06

  35. The Gauss Rifle http://www.scitoys.com/scitoys/scitoys/magnets/gauss.html Automata '06

  36. Operation of Gauss Rifle http://www.scitoys.com/scitoys/scitoys/magnets/gauss.html It Amplifies! Automata '06

  37. Our Own Gauss Rifle Automata '06

  38. Signal Propagation by Gauss Rifle Potential Energy Decreases Not reusable unless initial state is restored To restore initial state pump energy in system Automata '06

  39. Toppling dominoes [Thanks to Jordi Cortadella] Automata '06

  40. Wire Output Input [Thanks to Jordi Cortadella] Automata '06

  41. OR gate Output A+B Input B Input A [Thanks to Jordi Cortadella] Automata '06

  42. Molecule Cascades -- IBM Heinrich, Lutz, Gupta, Eigler, Science, 15 Nov 2002, pp. 1381-1387 http://domino.research.ibm.com/Comm/bios.nsf/pages/cascade.html Hopping CO molecules on Cu(111) surface Automata '06

  43. Tilting of Molecules Repulsive O C Cu Attractive (side view) (top view) [Carmona et al., 2006] CO molecules next to each other are repulsed. Depending on presence of other CO molecules, this may result in one moving away from the other Automata '06

  44. Linked Chevron Cascade -- IBM Automata '06

  45. “AND”-Gate -- IBM Input X Output Input Y Automata '06

  46. “OR”-Gate -- IBM Output Input X Input Y Automata '06

  47. Scanning Tunneling Microscope (STM) • Tunneling rate extremely sensitive to distance changes • Can also pick up atoms or molecules Michael Schmid, IAP/TU Wien Automata '06

  48. Molecule Cascade Video -- IBM http://domino.research.ibm.com/Comm/bios.nsf/pages/cascade.html Automata '06

  49. Three-input sorter Area: 200 nm2 (545 CO molecules) Equivalent CMOS circuit: 53µm2 260,000 times smaller !!! Moore’s law: 45 years to achieve the same size Delay: ~ 1 hour at 5 K [Thanks to Jordi Cortadella] Automata '06

  50. Molecule Cascade Challenges • Only one-time computing • Reinitialize after operation • …or reverse operation? • Finding suitable configurations Joint work with Jordi Cortadella’s group at University Polytecnica Cataluniya, Spain Automata '06

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