Von Neumann’s Von Neumann’s Automaton and Automaton and

VirusesVirusesMost slides taken fromWeizmann Institute of Science andRensselaer Polytechnic Institute

The General Question

What kind of logical organization is

sufficient for an automaton to control

itself in such a manner that it

reproduces itself?

Von Neumann Neighborhood

2

3 1 5

4

State of the cell at time t+1is calculable from its state and its

four non-diagonal neighboring cellsat time t.

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.

000 000

000 000

0 0000 0

unexcited unexcited unexcited unexcited unexcited unexcited

0 0signal 001 0

t

excited unexcited unexcited unexcited unexcited unexcited

000 0

t+1

10

unexcited excited unexcited unexcited unexcited unexcited

000 0

t+2

10

unexcited excited unexcited unexcited unexcited unexcited

000 0

t+3

10

unexcited unexcited excited unexcited unexcited unexcitedunexcited unexcited unexcited excited unexcited unexcited

000 0

t+4

0 1

unexcited unexcited unexcited unexcited excited unexcited

100 0

t+5

0 0

unexcited unexcited unexcited unexcited unexcited excited

000 1

t+6

0 0 000 0

t+7

0 0 1

unexcited unexcited unexcited unexcited unexcited unexcited

000 0

t+8

0 0 0

unexcited unexcited unexcited unexcited unexcited unexcited

Ordinary Transmission States

4 unexcited states 4 excited states

signal

Quiescent State

Cells in the quiescent state U

have to be excited with more

than one signal directed to them.

signal

cell in the

quiescent state cell in the ordinary

transmission state

Confluent States

C 0 0

u n e xc ite d s ta te

C 0 1

e xc ite d s ta te

C 1 0

e xc ite d s ta te

C 1 1

e xc ite d s ta te

C X Y

X sp e c ify in g th e cu r re n t s ta teY th e n e x t s ta te

C000

1C00

C01

C100

1

C11

C000

1

C01

C100

1

C11

C10 and C01

C00

t C10

t+2

C01

t+1 C00

t+3

Cell in confluent state directs signal to theneighboring cells not pointing to it.

C000

1C00

C01

C100

1

C11

C000

1

C01

C100

1

C11

C00

t

C00

C00

t+1 C00

t+2 C00

t+3

All of the cells in ordinary transmission states pointing to cell in confluent state have to be

excited.

A not excited cell at the input of a confluent cell

C11

C01

t

C01

t C11

t+1 C10

t+2 C00

t+3Two dots inside

The number of dots in = the number of dots out

C000

1C00

C01

C100

1

C11

C000

1

C01

C100

1

C11

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.

input

output

at time t

at time t+ through t+ +n

C

Pulser(10101)

C

C C

t+5

excited signal 01

tt+1

10

t+2t+4

10

t+3

01

t+6

01

t+7

01

10

t+8

10

t+14

1

t+12

1

t+10

1

t+11

0

t+13

0

t+9

Decoder(1x1x1)A decoder produces a single signal if the sequence

it receives has signals in specified positions.

C C C

C C C 01

t

excited signal 10

t+1

excited signal

t+201

t+310 01excited signal

t+41001

t+50110

t+610 01

01

t+701 10

10

t+801

01

10

t+910

1001

t+1001

t+1110

10 01

t+12

10

t+13

01

t+14

10

t+15t+16

01

t+17

10

t+18

1

t+19

Repeater

C signal 01 10

1 10 01

1

Repeater repeats the sequence of signals untilit is turned off.

destruction processconstruction process

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

The Destruction Process

The destruction process transforms unexcited

and excited states into the quiescent state in

single step.

C10

t t+1

Sensitive States

S 0 S 0 S 1 S 0 0 S 0 1 S 1 1 S 0 0 0

S

They are intermediary states converting quiescent state into one of the 9 unexcited states

C00

The Sensitized Tree

S0

1

0

10

1S11

01

0

1

U S0

S1

S10

C00

0

1

S00

S0110

S0000

0

1

1

U S0

S1

S10

quiescent state

The Construction Process

t

S10

t+3

S100

t+4

t+5

S0

t+1

t+2

S1

t

S10

t+3

S100

t+4 t+5

S0

t+1 t+2

S1

S0

10

10

1 S1

1

01

0

1

U S0

S1

S1

0

C0

0

01

S0

0S0

1

10

S00

00

0

1

1

U S0

S1

S1

0quiescent state

Periodic Pulser

P(11111)

RepeaterP(10101)

C

C

C

C

C C C C C C

C

C

C

C

C

C

C

C

C

C

C

C

C

C C

C

C

C

C C

C 1

C

C 0

C

C 1

C

C

S0

C

S1S11S111

C

C signal

signal

Coded Channel

D=decoder

P=pulser

Transition And Output Table

Automaton

o0=s0, etc

Finite Automaton

Constructing Arm

Horizontal Advance

Horizontal Advance of Constructing Arm

Vertical Advance of Constructing Arm

Horizontal Retreat of Constructing Arm

Vertical Retreat of Constructing Arm

Injection of Starting Stimulus

Reading Loop

Constructing Arm

Universal Computer

Universal Constructor

Automata Self-reproduction

Automata Self-reproduction

Automata Self-reproduction

Cellular Automata vs Viruses

Cellular Artificial Life

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

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

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

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

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 < major flaw in theory

References• J. Beuchat, J. Haenni, Von Neumann’s 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 Neumann’s 29-state cellular automaton, IEEE Proc. Supercomput.,1989.