Von Neumann’s Automaton and Viruses Most slides taken from Weizmann Institute of Science and Rensselaer 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 State of the cell at time t+1 is calculable from its state and its four non-diagonal neighboring cells at 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 unexcited 00 signal 0010 t excitedunexcited 0000 t+1 10 unexcited excitedunexcited 0000 t+2 10 unexcitedexcitedunexcited 0000 t+3 10 unexcited excitedunexcited excitedunexcited 0000 t+4 01 unexcited excitedunexcited 1000 t+5 00 unexcited excited 0001 t t unexcited 0000 t 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 C 01 C C 11 C C 01 C C 11

C 10 and C 01 C 00 t C 10 t+2 C 01 t+1 C 00 t+3 Cell in confluent state directs signal to the neighboring cells not pointing to it. C C 01 C C 11 C C 01 C C 11

C 00 t t+1 C 00 t+2 C 00 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

C 11 C 01 t t C 11 t+1 C 10 t+2 C 00 t+3 Two dots inside The number of dots in = the number of dots out C C 01 C C 11 C C 01 C C 11

Pulser A pulser P(i 1, i 2,…, i n ) is used to encode a sequence of signals so that a single excited signal entering the input cell will produce the sequence i 1, i 2,…, i n at the output cell. input output at time t at time t+ through t+ +n

C Pulser(10101) C CC t+5 excited signal 01 tt+1 10 t+2 t+4 10 t+3 01 t+6 01 t 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. CCC CCC 01 t excited signal 10 t+1 excited signal t+2 01 t excited signal t t t t t t t t t t t t+15t t t+18 1 t+19

Repeater C signal Repeater repeats the sequence of signals until it is turned off. destruction process construction process

Special Transmission States 4 unexcited states 4 excited states They are similar in operation to ordinary transmission states, but they convert confluent 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. C 10 tt+1

Sensitive States They are intermediary states converting quiescent state into one of the 9 unexcited states C 00

The Sensitized Tree S0S S US0S0 S1S1 S 10 C S 00 S S US0S0 S1S1 S 10 quiescent state

The Construction Process t S 10 t+3 S 100 t+4t+5 S0S0 t+1 t+2 S1S1

t S 10 t+3 S 100 t+4t+5 S0S0 t+1 t+2 S1S1 S0S S11S US0S0 S1S1 S10S10 C00C S00S00 S01S S US0S0 S1S1 S10S10 quiescent state

Periodic Pulser P(11111) Repeater P(10101) C C C C CCCCC C C C C C C C C C C C C C C CC C C C C C C 1 C C 0 C C 1 C C S0S0 C S1S1 S 11 S 111 C C 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

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, 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.