Von Neumann’s Automaton and Viruses

1. Von Neumann’s Automaton and Viruses Most slides taken from Weizmann Institute of Science and Rensselaer Polytechnic Institute

2. The General Question What kind of logical organization is sufficient for an automaton to control itself in such a manner that it reproduces itself?

3. Von Neumann Neighborhood 2 State of the cell at time t+1is calculable from its state and its four non-diagonal neighboring cellsat time t. 3 1 5 4

4. 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. 0 1 0 0 0 0 t+1 excited unexcited unexcited unexcited unexcited unexcited 1 0 0 0 0 0 signal unexcited unexcited unexcited unexcited unexcited unexcited t 0 0 0 0 0 0 0 0 0 0 0 0 unexcited unexcited unexcited excited unexcited unexcited unexcited unexcited excited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited excited unexcited unexcited unexcited unexcited 0 0 0 1 0 0 0 0 0 0 0 0 unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited unexcited excited unexcited excited 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 unexcited excited unexcited unexcited unexcited unexcited 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 t+4 0 0 0 0 t+8 t+7 t+3 t+5 t+6 t+2 States in Von Neumann Automaton

5. signal Ordinary Transmission States 4 unexcited states 4 excited states

6. signal Quiescent State cell in the ordinary transmission state cell in the quiescent state Cells in the quiescent stateU have to be excitedwith more than one signaldirected to them.

7. C00 C00 0 0 C00 C10 1 1 0 C01 C01 1 C10 0 C11 1 C11 Confluent States

8. C00 C01 C10 C00 t+1 t+2 t+3 Cell in confluent statedirects signal to the neighboring cells not pointing to it. C00 0 0 C00 C10 1 1 0 C10 and C01 C01 C01 1 C10 0 C00 C11 1 C11 t

9. C00 C00 t C00 t+1 C00 t+2 t+3 A not excited cell at the input of a confluent cell C00 All of the cells in ordinary transmission states pointing to cell in confluent state have to be excited.

10. C00 C01 C00 0 0 C00 C11 C10 t 1 1 0 C10 C01 t+1 C01 C00 1 C10 t+2 0 C11 t+3 1 C11 C11 C01 t Two dots inside The number of dots in = the number of dots out

11. Pulser output A pulser P(i1, i2 ,…, in) isused to encode a sequence of signals so that a single excited signalentering the input cell will produce the sequencei1, i2 ,…, in at the output cell. at time t+ through t+ +n input at time t

12. 10 t+1 1 0 1 0 1 10 01 excited signal 10 01 10 01 t+2 01 t+14 t+9 t+10 t+13 t+8 t+6 t+5 t+7 t+4 t+3 t+11 t t+12 Pulser(10101) C C C C

13. C C C 1 01 10 01 10 01 10 10 10 01 01 10 01 excited signal excited signal excited signal C C C 10 10 01 01 01 10 10 01 01 10 01 10 10 01 01 10 01 10 t+6 t+5 t+4 t+3 t+11 t+1 t t+8 t+2 t+9 t+15 t+19 t+7 t+14 t+16 t+13 t+17 t+18 t+12 t+10 Decoder(1x1x1) A decoder produces a single signal if the sequence it receives has signals in specified positions.

14. 1 1 C signal destruction process Repeater repeats the sequence of signals until it is turned off. Repeater 10 10 01 01 construction process

15. Special Transmission States 4 unexcited states 4 excited states They are similar in operation to ordinarytransmission states, but they convertconfluent states toquiescent state. Special transmission states are denoted by double arrow notation

16. C10 The Destruction Process The destruction process transforms unexcited and excited statesinto the quiescent state in single step. t t+1

17. Sensitive States They are intermediary states converting quiescent state into one of the 9 unexcited states C00

18. 0 S000 1 0 1 S00 0 0 S01 S0 1 1 0 0 U U 1 S0 S0 S10 S10 1 0 quiescent state 1 S1 S1 0 1 S11 1 C00 The Sensitized Tree

19. S0 S1 t+1 t+2 S10 S100 t+3 t+4 t+5 The Construction Process t

20. 0 S000 1 S0 0 1 S00 S1 t 0 0 S01 S0 1 t+1 1 t+2 0 0 U U 1 S0 S0 S10 S10 1 S10 0 S100 quiescent state 1 S1 S1 0 1 t+3 S11 t+4 1 C00 t+5

21. C C C C C C C C C C C C C C C C signal S0 S11 S1 C C C C C 1 0 1 C C C C C C C C signal Periodic Pulser C C C C C C P(11111) S111 C C P(10101) Repeater C C C

22. Coded Channel D=decoder P=pulser

23. Transition And Output Table

24. Automaton o0=s0, etc

25. Finite Automaton

26. Constructing Arm

27. Horizontal Advance

28. Horizontal Advance of Constructing Arm

29. Vertical Advance of Constructing Arm

30. Horizontal Retreat of Constructing Arm

31. Vertical Retreat of Constructing Arm

32. Injection of Starting Stimulus

33. Reading Loop

34. Constructing Arm

35. Universal Computer

36. Universal Constructor

37. Automata Self-reproduction

38. Automata Self-reproduction

39. Automata Self-reproduction

40. Cellular Automata vs Viruses Cellular Artificial Life

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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.