Reconfigurable Asynchronous Logic Automaton

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Reconfigurable AsynchronousLogic Automaton

• David Dalrymple
• Erik Demaine
• Neil Gershenfeld

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Reconfigurable AsynchronousLogic Automata
stem
(RALA)
wire
XOR
crossover
OR
delete
David Dalrymple Erik Demaine Neil Gershenfeld
NAND
copy
AND
wire
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Motivation for Theoreticians

• What is the model of computation of the physical
  universe?
• Computation local interaction of particles
• Particles move around (which takes time)
• Very different from existing models
• Sequential models of computation (RAM, etc.)
• Memory hierarchies model movement to a single
  CPU, but this is an unnecessarily limit
• PRAM/UMA ignores communication cost
• Most distributed computing ignores geometry

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Motivation for Systems
80-core TeraflopIntel Polaris

• Evolution increasingly multicore
• What happens in the limit?
• FPGAs highly successful
• What happens in the limit?
• Is there a universal chip architecture supporting
  general algorithms nearly as efficiently as all
  other chips?

XILINX FPGA
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Motivation for Fabrication

• How should computation scale tophysically large
  objects?
• Walls
• Displays
• Surfaces
• 3D print
• Robots

Solar furnace in Odellio, France.
Temperaturesup to 33,000 C.
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Ideas Behind RALA
computation data shape communication

• Unify computation data to equal bits
• Embed into geometric space
• Communicate subject to physical laws
• Essentially a general circuit, wherelonger wires
  take longer to carry data
• Globally asynchronous to enable scaling,but
  locally synchronous for ease of use
• Reconfigurable to enable programming

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Asynchronous Logic Automaton (ALA)

• Circuit grid of cells (squares or cubes)
• Single-bit stream processor
• Up to two inputs
• Any number of outputs
• Wires between neighbors
• Buffers a single bit (0 or 1)
• Can have no bits (X)
• Gate operates when allinputs are ready (0 or
  1) outputs are free (X)

AND
OR
X
1
X
0
X
X
1
0
XOR
OR
X
1
X
X
1
0
1
NAND
OR
1
X
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ALA
1
0
X
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ALA is Easy to Program(similar to standard
digital circuits)
SEA cryptosystem
sorter
multiplier
router(project with Cisco)
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Reconfiguration in RALA

• Stem cell turns data into programs by
  reprogramming neighbors itself
• Format of input stream (from one source)
• Direction (3 bits) make neighbor a stem cell
• Forward bits to neighbor until it says done
• Cell type (3 bits) AND, NAND, OR,XOR,
  crossover, copy, delete, stem
• Input directions (3 bits ? 2 inputs)
• Output directions (6 bits)
• Repeat (or special 000 code ? done)

NAND
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How to Make Anything with RALA

• Circuit rasterization
• Zig-zag through target circuit region using
  forwarding mechanism of stem cell
• (requires region to have a Hamiltonian path)
• Send code to program cells in reverse order

Stem
Stem
forward
right
right
left
left
OR,B,L,L
NAND,F,L,B
OR,L,N,BR
XOR,R,F,B
AND,B,R,F
OR,R,N,F
AND
OR
Stem
Stem
OR
XOR
Stem
Stem
OR
NAND
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CAD ?RALA
cad.py
face circle(0,0,10) eye circle(0,0,2) face
subtract(face, move(eye,4,3)) face
subtract(face,
move(eye,-4,3)) mouth circle(0,0,8) mouth
subtract(mouth,
circle(0,0,6)) mouth subtract(mouth,
rectangle(-10,10,-2,10)) face
subtract(face,mouth)
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CAD ?RALA
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CAD ? RALA (3D)
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How to Make Anything with RALA

• Spanning-tree method
• Perform depth-first search of spanning tree of
  target circuit
• Use backtracking ability of stem-cell forwarding
• More general, e.g., if no Hamiltonian path (or
  dont want to find one)

AND
OR
OR
XOR
OR
NAND
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Hierarchical Construction

• Exploit computational power to build structures
  faster, e.g., hierarchically

code 3 ( right left straight 2
stem(B) wire(L,F,B) null)
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Regular Grid Construction
prefix (right stem(B) forward x) (m -
1) right stem(B) wire(B,R) (wire(B,F)
(x - 1) wire(B,F,R)) (m - 1) (left
stem(B) forward y) (n - 1) left stem(B)
wire(B,L) (wire(B,F) (y - 1)
wire(B,F,L)) (n - 1)
unit
unit
unit

• Theorem m n array ofx y modules in timeO(m
  n x y) vs. O(m n x y)
• E.g. exploit regularity of memory, adder, shape

unit
unit
unit
unit
unit
unit
unit
unit
unit
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Replication
code right right left stem(B)
wire(B,F,L) wire(R,L) forward forward

• 81-bit string encodesuniversal replicator
• Replicates givenprogram infinitely
• polymeraseribosome

replicator
stem
program
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Cellular Automata
alive (2 num_live_neighbors 3)

• Conways Game of Life is Turing-complete

Gospers Glider Gun
1714?1647 Turing machine
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1966
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RALA vs. Cellular Automata

• Logic automaton
• Designed for digital Boolean logic
• Easy to implement standard circuits
• Asynchronous
• Cellular automata require global clock
• Impractical/slow for large sizes
• Reconfigurable
• Stem cell converts data into programs
• vs. von Neumann gates enable replicationbut not
  obviously universal ribosome

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Programmable Matter via RALA

• Cell one-bit computer (gate) one unit
  of physical space
• Communicates with neighbors
• Request new cell on bare face
• ? Can grow a shape
• Convergence of shape,computation,
  andcommunication

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RALA Convergence of Shape, Computation,
Communication

• New model for mixing computation, data, program,
  shape (state space time logic)
• Theoretically interesting
• Parallel in a new way
• Computation embedded into geometry
• Programs that generate programs (and so on) opens
  new doors for construction, encoding,
• Practically interesting
• Physically realistic (pay for transportation)
• Easy to build (next)

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Reconfigurable AsynchronousLogic Automata
1 0 x
Dalrymple, Demaine, Gershenfeld 2009
stem
wire
XOR
crossover
space time state logic
OR
delete
NAND
copy
ps vs. fs/µ ? ns/mm
AND
wire
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Reconfigurable AsynchronousLogic Automata
stem
(RALA)
wire
XOR
crossover
OR
delete
David Dalrymple Erik Demaine Neil Gershenfeld
NAND
copy
AND
wire