Von Neumann

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Von Neumanns Automaton and Viruses
Most slides taken from Weizmann Institute of
Science and Rensselaer Polytechnic Institute
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The General Question

• What kind of logical organization is
• sufficient for an automaton to control
• itself in such a manner that it
• reproduces itself?

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Von Neumann Neighborhood
2
State of the cell at time t1is calculable from
its state and its four non-diagonal neighboring
cellsat time t.
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1
5
4
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States in Von Neumann Automaton

• Each cell is capable of 29 different states.
• Each state is excited or unexcited.
• Movement of data on the cellular lattice is
  determined by the changes of unexcited and
  excited states in cell.
• Cells change at discrete times according to the
  transition rule.

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Ordinary Transmission States
4 unexcited states
4 excited states
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Quiescent State
cell in the quiescent state
cell in the ordinary transmission
state

• Cells in the quiescent state U
• have to be excited with more
• than one signal directed to them.

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Confluent States
8
C10 and C01
C00
C00
0
0
C00
C10
1
1
0
C01
C01
1
C10
0
C00
C11
1
C11
t
9
C00
A not excited cell at the input of a confluent
cell
All of the cells in ordinary transmission states
pointing to cell in confluent state have to
be excited.
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C11
C01
t
Two dots inside
The number of dots in the number of dots out
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Pulser

• A pulser P(i1, i2 ,, in) is used to encode a
  sequence of signals so that a single excited
  signal entering the input cell will produce the
  sequence i1, i2 ,, in at the output cell.

output
at time t through t n
input
at time t
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Pulser(10101)
C
C
C
C
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Decoder(1x1x1)

• A decoder produces a single signal if the
  sequence it receives has signals in specified
  positions.

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Repeater
Repeater repeats the sequence of signals until it
is turned off.
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10
01
01
construction process
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Special Transmission States
4 unexcited states
4 excited states
They are similar in operation to
ordinarytransmission states, but they
convertconfluent states to quiescent state.
Special transmission states are denoted by double
arrow notation
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The Destruction Process

• The destruction process transforms unexcited
• and excited states into the quiescent state in
• single step.

t
t1
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Sensitive States
They are intermediary states converting quiescent
state into one of the 9 unexcited states
C00
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The Sensitized Tree
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The Construction Process
t
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(No Transcript)
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Periodic Pulser
C
C
C
C
C
C
P(11111)
C
S111


C
P(10101)

Repeater

C
C
C
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Coded Channel
Ddecoder Ppulser
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Transition And Output Table
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Automaton
o0s0, etc
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Finite Automaton
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Constructing Arm
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Horizontal Advance
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Horizontal Advance of Constructing Arm
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Vertical Advance of Constructing Arm
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Horizontal Retreat of Constructing Arm
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Vertical Retreat of Constructing Arm
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Injection of Starting Stimulus
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Reading Loop
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Constructing Arm
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Universal Computer
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Universal Constructor
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Automata Self-reproduction
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Automata Self-reproduction
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Automata Self-reproduction
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Cellular Automata vs Viruses

• Cellular Artificial Life

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Virus Definition

• A simple computer program that attaches itself to
  a legitimate executable program, and reproduces
  itself when the program is run.
• Trojan Horse no self-replication
• Worm infects through security hole, then
  self-replicates through idle memory

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Virus Types

• Boot sector viruses
• Infects boot sector on diskette
• Replaces it with replicated copy of virus
• Hides in memory, infects all new disks
• Executable Viruses
• Resident, direct action or a combination
• Resident remains in memory and attacks every
  program run
• Direct action may search for a new file to infect

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Virus Categories

• Parasitic spread on program execution through
  storage and transmission medium
• Multipartite infects both boot sector and
  executables
• Stealth hidden in memory to infect or redirect
  interrupts
• Polymorphic uses encryption to change signature
  for each replica
• Dropper places boot sector infector on disk

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Computer vs. Biology

• String of genetic material vs. instruction set
• Neither capable of self-replication outside of a
  host
• Takes over cell and uses it to spread virus
• Unexpected and uncontrollable replication makes
  viruses (of either type) dangerous

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Virus vs. Alife

• Patterns in space-time
• Self reproduction
• Information storage of self representation
• Metabolism
• Functional interaction with environment
• Interdependence of parts
• Stability under perturbations
• Growth
• Evolution lt major flaw in theory

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References

• J. Beuchat, J. Haenni, Von Neumanns 29-State
  Cellular Automaton A Hardware Implementation,
  IEEE Transactions On Education, Vol. 43, No. 3,
  2000.
• A.W.Burks, Von Neumann Self-Reproducing Automata,
  Essay 1 from Essays on Cellular Automata.
• J.Signorini, How a SIMD machine can implement a
  complex cellular automaton? A case study von
  Neumanns 29-state cellular automaton, IEEE Proc.
  Supercomput.,1989.