Fina lminimisationcinder4

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JNTU QUALITATIVE VISUAL ALGORITHMS

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Fina lminimisationcinder4

  1. 1. Problem 4
  2. 2. Problem 4 ‘AA’ ‘BB’ ‘CC’ ‘DD’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  3. 3. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘CC’ ‘DD’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  4. 4. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘CC’ ‘DD’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  5. 5. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  6. 6. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  7. 7. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘FF’ ‘GG’ ‘HH’
  8. 8. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘HH’
  9. 9. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘HH’
  10. 10. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’
  11. 11. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  12. 12. Problem 4 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘AA’ ‘BB’ ‘AA’ ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  13. 13. Problem 4 ‘0’ ‘1’• WE WILL USE ‘AA’ ‘BB’ ‘AA’ THE GRAPH COLORING ‘BB’ ‘AA’ ‘CC’ ALGORITHM ‘CC’ ‘DD’ ‘BB’ FOR THE ‘DD’ ‘DD’ ‘AA’ MINIMISATION ‘EE’ ‘DD’ ‘FF’ OF THE FINITE ‘FF’ ‘GG’ ‘EE’ AUTOMATA ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  14. 14. Problem 4 ‘0’ ‘1’• WE WILL USE THE GRAPH COLORING ‘AA’ ‘BB’ ‘AA’ ALGORITHM FOR ‘BB’ ‘AA’ ‘CC’ THE MINIMISATION ‘CC’ ‘DD’ ‘BB’ OF THE FINITE AUTOMATA ‘DD’ ‘DD’ ‘AA’• COLOR THE FINAL ‘EE’ ‘DD’ ‘FF’ STATES ONE ‘FF’ ‘GG’ ‘EE’ COLOR ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  15. 15. Problem 4 ‘0’ ‘1’• WE WILL USE THE GRAPH COLORING ‘AA’ ‘BB’ ‘AA’ ALGORITHM FOR THE MINIMISATION ‘BB’ ‘AA’ ‘CC’ OF THE FINITE AUTOMATA ‘CC’ ‘DD’ ‘BB’• COLOR THE FINAL ‘DD’ ‘DD’ ‘AA’ STATES ONE COLOR ‘EE’ ‘DD’ ‘FF’• COLOR OTHER ‘FF’ ‘GG’ ‘EE’ STATES SOME OTHER COLOR ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  16. 16. Problem 4 ‘0’ ‘1’• WE WILL USE THE GRAPH COLORING ‘AA’ ‘BB’ ‘AA’ ALGORITHM FOR THE MINIMISATION OF THE ‘BB’ ‘AA’ ‘CC’ FINITE AUTOMATA• COLOR THE FINAL ‘CC’ ‘DD’ ‘BB’ STATES ONE COLOR ‘DD’ ‘DD’ ‘AA’• COLOR OTHER STATES SOME OTHER COLOR ‘EE’ ‘DD’ ‘FF’• MARK THE FINAL STATES ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  17. 17. Problem 4 ‘0’ ‘1’• CALL THE NON- ‘AA’ ‘BB’ ‘AA’ FINAL STATE ‘BB’ ‘AA’ ‘CC’ COLOR THE ‘CC’ ‘DD’ ‘BB’ HOME COLOR ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  18. 18. Problem 4 ‘0’ ‘1’• CALL THE NON- ‘AA’ ‘BB’ ‘AA’ FINAL STATE ‘BB’ ‘AA’ ‘CC’ COLOR THE ‘CC’ ‘DD’ ‘BB’ HOME COLOR ‘DD’ ‘DD’ ‘AA’• ON A ‘0’ DAY ‘CC’ ‘EE’ DO ‘EE’ ‘DD’ ‘FF’ NOT WANT TO ‘FF’ ‘GG’ ‘EE’ STAY AT HOME. ‘GG’ ‘FF’ ‘GG’ THEY WANT TO ‘HH’ ‘GG’ ‘DD’ PARTY AT ‘DD’
  19. 19. Problem 4 ‘0’ ‘1’• CALL THE NON- FINAL STATE ‘AA’ ‘BB’ ‘AA’ COLOR THE HOME ‘BB’ ‘AA’ ‘CC’ COLOR• ON A ‘0’ DAY ‘CC’ ‘CC’ ‘DD’ ‘BB’ ‘EE’ DO NOT WANT ‘DD’ ‘DD’ ‘AA’ TO STAY AT HOME. THEY WANT TO ‘EE’ ‘DD’ ‘FF’ PARTY AT ‘DD’ ‘FF’ ‘GG’ ‘EE’• OTHERS AT HOME DISAGREE ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  20. 20. Problem 4 ‘0’ ‘1’ ON A ‘0’ DAY ‘CC’ ‘AA’ ‘BB’ ‘AA’ ‘EE’ DO NOT WANT ‘BB’ ‘AA’ ‘CC’ TO STAY AT HOME. ‘CC’ ‘DD’ ‘BB’ THEY WANT TO PARTY AT ‘DD’ ‘DD’ ‘DD’ ‘AA’• OTHERS AT HOME ‘EE’ ‘DD’ ‘FF’ DISAGREE ‘FF’ ‘GG’ ‘EE’• GIVE ‘CC’ & ‘EE’ ‘GG’ ‘FF’ ‘GG’ ANOTHER COLOR ‘HH’ ‘GG’ ‘DD’
  21. 21. Problem 4 ‘0’ ‘1’ ON A ‘0’ DAY ‘CC’ ‘EE’ DO NOT WANT ‘AA’ ‘BB’ ‘AA’ TO STAY AT HOME. ‘BB’ ‘AA’ ‘CC’ THEY WANT TO ‘CC’ ‘DD’ ‘BB’ PARTY AT ‘DD’• OTHERS AT HOME ‘DD’ ‘DD’ ‘AA’ DISAGREE ‘EE’ ‘DD’ ‘FF’• GIVE ‘CC’ & ‘EE’ ‘FF’ ‘GG’ ‘EE’ ANOTHER COLOR ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  22. 22. Problem 4 ‘0’ ‘1’ ON A ‘1’ DAY ‘AA’ & ‘GG’ WANT TO ‘AA’ ‘BB’ ‘AA’ STAY AT HOME ‘BB’ ‘AA’ ‘CC’‘BB’ & ‘FF’ WANT TO ‘CC’ ‘DD’ ‘BB’ JOIN ‘CC’ & ‘EE’ ANOTHER COLOR ‘DD’ ‘DD’ ‘AA’‘HH’ IS ALONE ‘EE’ ‘DD’ ‘FF’ WANTING TO GO ‘FF’ ‘GG’ ‘EE’ TO THE PARTY AT ‘DD’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  23. 23. Problem 4 ‘0’ ‘1’ 1.ON A ‘1’ DAY ‘AA’ ‘AA’ ‘BB’ ‘AA’ & ‘GG’ WANT TO STAY AT HOME ‘BB’ ‘AA’ ‘CC’2.‘BB’ & ‘FF’ WANT ‘CC’ ‘DD’ ‘BB’ TO JOIN ‘CC’ & ‘EE’ ANOTHER COLOR ‘DD’ ‘DD’ ‘AA’3.‘HH’ IS ALONE ‘EE’ ‘DD’ ‘FF’ WANTING TO GO TO THE PARTY AT ‘FF’ ‘GG’ ‘EE’ ‘DD’ ‘GG’ ‘FF’ ‘GG’ALL THREE GROUPS ‘HH’ ‘GG’ ‘DD’ HAVE DIFFERENT COLORS
  24. 24. Problem 4 ‘0’ ‘1’ 1.ON A ‘1’ DAY ‘AA’ & ‘GG’ WANT TO ‘AA’ ‘BB’ ‘AA’ STAY AT HOME2.‘BB’ & ‘FF’ WANT ‘BB’ ‘AA’ ‘CC’ TO JOIN ‘CC’ & ‘EE’ ‘CC’ ‘DD’ ‘BB’ ANOTHER COLOR3.‘HH’ IS ALONE ‘DD’ ‘DD’ ‘AA’ WANTING TO GO TO THE PARTY AT ‘EE’ ‘DD’ ‘FF’ ‘DD’ ‘FF’ ‘GG’ ‘EE’ALL THREE GROUPS HAVE DIFFERENT ‘GG’ ‘FF’ ‘GG’ COLORS ‘HH’ ‘GG’ ‘DD’
  25. 25. Problem 4 ‘0’ ‘1’ 1.’AA’ AND ‘GG’ ‘AA’ ‘BB’ ‘AA’ AGREE ON BOTH ‘BB’ ‘AA’ ‘CC’ DAYS ‘0’ OR ‘1’ ‘CC’ ‘DD’ ‘BB’2.‘BB’ & ‘FF’ AGREE ‘DD’ ‘DD’ ‘AA’ ON BOTH DAYS ‘0’ AND ’1’ ‘EE’ ‘DD’ ‘FF’3.’CC’ AND ‘EE’ ‘FF’ ‘GG’ ‘EE’ AGREE ON BOTH ‘GG’ ‘FF’ ‘GG’ DAYS ‘0’ AND ‘1’ ‘HH’ ‘GG’ ‘DD’4. ‘DD’ IS A LONER
  26. 26. Problem 4 ‘0’ ‘1’THE MINIMAL ‘AA’ ‘BB’ ‘AA’ MACHNE HAS 4 STATES AND IS ‘BB’ ‘AA’ ‘CC’ AS GIVEN ‘CC’ ‘DD’ ‘BB’ ALONGSIDE ‘DD’ ‘DD’ ‘AA’ ‘EE’ ‘DD’ ‘FF’ ‘FF’ ‘GG’ ‘EE’ ‘GG’ ‘FF’ ‘GG’ ‘HH’ ‘GG’ ‘DD’
  27. 27. Problem 5
  28. 28. Problem 5‘AA’‘BB’‘CC’‘DD’‘EE’‘FF’‘GG’‘HH’‘II’
  29. 29. Problem 5 ‘0’ ‘1’‘AA’‘BB’‘CC’‘DD’‘EE’‘FF’‘GG’‘HH’‘II’
  30. 30. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’‘CC’‘DD’‘EE’‘FF’‘GG’‘HH’‘II’
  31. 31. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’‘DD’‘EE’‘FF’‘GG’‘HH’‘II’
  32. 32. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’‘EE’‘FF’‘GG’‘HH’‘II’
  33. 33. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’‘FF’‘GG’‘HH’‘II’
  34. 34. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’‘GG’‘HH’‘II’
  35. 35. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’‘HH’‘II’
  36. 36. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’ ‘HH’ ‘BB’‘HH’‘II’
  37. 37. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’ ‘HH’ ‘BB’‘HH’ ‘II’ ‘CC’‘II’
  38. 38. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’ ‘HH’ ‘BB’‘HH’ ‘II’ ‘CC’‘II’ ‘AA’ ‘EE’
  39. 39. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’ ‘HH’ ‘BB’‘HH’ ‘II’ ‘CC’‘II’ ‘AA’ ‘EE’
  40. 40. Problem 5 ‘0’ ‘1’‘AA’ ‘BB’ ‘EE’‘BB’ ‘CC’ ‘FF’‘CC’ ‘DD’ ‘HH’‘DD’ ‘EE’ ‘HH’‘EE’ ‘FF’ ‘II’‘FF’ ‘GG’ ‘BB’‘GG’ ‘HH’ ‘BB’‘HH’ ‘II’ ‘CC’‘II’ ‘AA’ ‘EE’
  41. 41. Problem 5 ‘0’ ‘1’ ‘AA’ ‘BB’ ‘EE’ ‘BB’ ‘CC’ ‘FF’ ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  42. 42. Problem 5WE WILL ‘0’ ‘1’MINIMISE THE ‘AA’ ‘BB’ ‘EE’FINITEAUTOMATA ‘BB’ ‘CC’ ‘FF’USING THE ‘CC’ ‘DD’ ‘HH’GRAPHCOLORING ‘DD’ ‘EE’ ‘HH’ALGORITHM ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  43. 43. Problem 5COLOR THE ‘0’ ‘1’FINAL STATES ‘AA’ ‘BB’ ‘EE’ANOTHERCOLOR ‘BB’ ‘CC’ ‘FF’THE OTHER ‘CC’ ‘DD’ ‘HH’STATES ARE IN ‘DD’ ‘EE’ ‘HH’THE HOMECOLOR ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  44. 44. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘EE’ & ‘HH’ WHOARE AT HOME ‘BB’ ‘CC’ ‘FF’WANT TO GOTO THE PARTY ‘CC’ ‘DD’ ‘HH’THE OTHERS ‘DD’ ‘EE’ ‘HH’AT HOME ARE ‘EE’ ‘FF’ ‘II’NOTINTERESTED ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  45. 45. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘EE’ & ‘HH’ WHOARE AT HOME ‘BB’ ‘CC’ ‘FF’WANT TO GOTO THE PARTY ‘CC’ ‘DD’ ‘HH’THE OTHERS ‘DD’ ‘EE’ ‘HH’AT HOME ARE ‘EE’ ‘FF’ ‘II’NOTINTERESTED ‘FF’ ‘GG’ ‘BB’GIVE ‘EE’ & ‘HH’ ‘GG’ ‘HH’ ‘BB’ANOTHER ‘HH’ ‘II’ ‘CC’COLOR ‘II’ ‘AA’ ‘EE’
  46. 46. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘EE’ & ‘HH’ WHO ‘AA’ ‘BB’ ‘EE’ARE AT HOMEWANT TO GO ‘BB’ ‘CC’ ‘FF’TO THE PARTY ‘CC’ ‘DD’ ‘HH’THE OTHERS ‘DD’ ‘EE’ ‘HH’AT HOME ARENOT ‘EE’ ‘FF’ ‘II’INTERESTED ‘FF’ ‘GG’ ‘BB’GIVE ‘EE’ & ‘HH’ ‘GG’ ‘HH’ ‘BB’ANOTHERCOLOR ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  47. 47. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘DD’ & ‘GG’ GO ‘AA’ ‘BB’ ‘EE’TO ‘EE’,’HH’ ‘BB’ ‘CC’ ‘FF’OTHERS ATHOME ‘CC’ ‘DD’ ‘HH’‘AA’,’BB’,’CC’ ‘DD’ ‘EE’ ‘HH’STAY PUT ATHOME ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  48. 48. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘DD’ & ‘GG’ GO ‘AA’ ‘BB’ ‘EE’TO ‘EE’,’HH’ ‘BB’ ‘CC’ ‘FF’OTHERS ATHOME ‘CC’ ‘DD’ ‘HH’‘AA’,’BB’,’CC’ ‘DD’ ‘EE’ ‘HH’STAY PUT ATHOME ‘EE’ ‘FF’ ‘II’GIVE ANOTHER ‘FF’ ‘GG’ ‘BB’COLOR TO ‘DD’ ‘GG’ ‘HH’ ‘BB’AND ‘GG’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  49. 49. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘CC’ GOES TO‘DD’ ANOTHER ‘BB’ ‘CC’ ‘FF’COLOR ‘CC’ ‘DD’ ‘HH’‘AA’, ‘BB’ STAYPUT AT HOME ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  50. 50. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘CC’ GOES TO ‘AA’ ‘BB’ ‘EE’‘DD’ ANOTHERCOLOR ‘BB’ ‘CC’ ‘FF’‘AA’, ‘BB’ STAY ‘CC’ ‘DD’ ‘HH’PUT AT HOME ‘DD’ ‘EE’ ‘HH’SO ‘CC’ GETS ‘EE’ ‘FF’ ‘II’ANOTHERCOLOR ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  51. 51. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘AA’ WANTS TOSTAY HOME ‘BB’ ‘CC’ ‘FF’BUT ‘BB’WANTS ‘CC’ ‘DD’ ‘HH’ANOTHER ‘DD’ ‘EE’ ‘HH’COLOR ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  52. 52. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘AA’ WANTS TO ‘AA’ ‘BB’ ‘EE’STAY HOMEBUT ‘BB’ ‘BB’ ‘CC’ ‘FF’WANTS ‘CC’ ‘DD’ ‘HH’ANOTHERCOLOR ‘DD’ ‘EE’ ‘HH’GIVE ‘BB’ ‘EE’ ‘FF’ ‘II’ANOTHER ‘FF’ ‘GG’ ‘BB’COLOR ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  53. 53. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘FF’ AND ‘II’WANT ‘BB’ ‘CC’ ‘FF’DIFFERENTCOLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  54. 54. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘FF’ AND ‘II’ ‘AA’ ‘BB’ ‘EE’WANTDIFFERENT ‘BB’ ‘CC’ ‘FF’COLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  55. 55. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘EE’ AND ‘HH’WANT ‘BB’ ‘CC’ ‘FF’DIFFERENTCOLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  56. 56. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘EE’ AND ‘HH’ ‘AA’ ‘BB’ ‘EE’WANTDIFFERENT ‘BB’ ‘CC’ ‘FF’COLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  57. 57. Problem 5 ‘0’ ‘1’ON A ‘0’ DAY ‘AA’ ‘BB’ ‘EE’‘DD’ AND ‘GG’WANT ‘BB’ ‘CC’ ‘FF’DIFFERENTCOLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  58. 58. Problem 5ON A ‘0’ DAY ‘0’ ‘1’‘DD’ AND ‘GG’ ‘AA’ ‘BB’ ‘EE’WANTDIFFERENT ‘BB’ ‘CC’ ‘FF’COLORS ‘CC’ ‘DD’ ‘HH’ ‘DD’ ‘EE’ ‘HH’ ‘EE’ ‘FF’ ‘II’ ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  59. 59. Problem 5 ‘0’ ‘1’SO JUST BY ‘AA’ ‘BB’ ‘EE’REPEATEDLYCONSIDERING ‘BB’ ‘CC’ ‘FF’‘0’ DAYS, DAYAFTER DAY WE ‘CC’ ‘DD’ ‘HH’FIND THAT ‘DD’ ‘EE’ ‘HH’EVERYONE HASBECOME A ‘EE’ ‘FF’ ‘II’SINGLETON ‘FF’ ‘GG’ ‘BB’ ‘GG’ ‘HH’ ‘BB’ ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’
  60. 60. Problem 5SO JUST BY ‘0’ ‘1’REPEATEDLY ‘AA’ ‘BB’ ‘EE’CONSIDERING‘0’ DAYS, DAY ‘BB’ ‘CC’ ‘FF’AFTER DAY WE ‘CC’ ‘DD’ ‘HH’FIND THATEVERYONE HAS ‘DD’ ‘EE’ ‘HH’BECOME A ‘EE’ ‘FF’ ‘II’SINGLETON ‘FF’ ‘GG’ ‘BB’THE AUTOMATAAS GIVEN IS ‘GG’ ‘HH’ ‘BB’MINIMAL ‘HH’ ‘II’ ‘CC’ ‘II’ ‘AA’ ‘EE’

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