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Design an Initial State Machine to Accept: (11+010)*(111)

Generate an initial design for a state machine to accept the pattern (11+010)*(111). Begin by creating an unreduced state table with nulls, then proceed to remove nulls, convert to deterministic, and rename states following specific rules. The final minimized machine is detailed, highlighting transitions and a black hole state. Our machine is tailored for the specified pattern.

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Design an Initial State Machine to Accept: (11+010)*(111)

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  1. Machine to Accept • (11+010)*(111)+

  2. Initial Design C H 1 1 1 λ G A λ D 0 1 1 0 E F 1 B

  3. 0 1 λ -> A B C D B E C A D F E A F G G H H D * State Table

  4. Complete Nulls • Nothing to do in this example

  5. 0 0 1 1 λ -> -> A A B B C CF D B B E E C C A A D D F F E E A A F F G G G G H H H H F D * * Remove nulls

  6. Convert to deterministic

  7. Rename

  8. 0 1 =0 0 1 =1 -> a b c 0 0 0 0 b d e 0 0 0 0 c d f 0 0 0 0 d d d 0 0 0 0 e a d 0 0 0 0 f b g 0 0 1 1 g d h 1 0 0 2 h b i 0 0 1 1 i d j 1 0 1 3 j b i 1 0 1 3 0 & 1 - equivalence

  9. 0 1 =1 0 1 =2 -> a b c 0 0 0 0 b d e 0 0 0 0 c d f 0 0 1 1 d d d 0 0 0 0 e a d 0 0 0 0 f b g 1 0 2 2 g d h 2 0 1 3 h b i 1 0 3 4 i d j 3 0 3 5 j b i 3 0 3 5 1 & 2 -equivalence

  10. 0 1 =2 0 1 =3 -> a b c 0 0 1 0 b d e 0 0 0 1 c d f 1 0 2 2 d d d 0 0 0 1 e a d 0 0 0 1 f b g 2 0 3 3 g d h 3 0 4 4 h b i 4 0 5 5 i d j 5 0 5 6 j b i 5 0 5 6 2 & 3 - equivalence

  11. 3 & 4 - equivalence

  12. 4 & 5 - equivalence

  13. 0 1 =5 0 1 =6 -> a b c 0 1 2 0 b d e 1 3 4 1 c d f 2 3 5 2 d d d 3 3 3 3 e a d 4 0 3 4 f b g 5 1 6 5 g d h 6 3 7 6 h b i 7 1 8 7 i d j 8 3 9 8 j b i 9 1 8 9 5 & 6 - equivalence

  14. State 0 1 -> 0 1 2 1 3 4 2 3 5 3 3 3 4 0 3 5 1 6 6 3 7 * 7 1 8 8 3 9 * 9 1 8 * Minimized machine

  15. 1 2 5 1 1 6 1 0 0 0 7 0 0 1 1 1 4 8 1 0 3 black hole 9 1 Our machine for (11+010)*(111)+

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