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Minimization of DFA with Subset Construction for Regular Expressions

This document explores the process of minimizing Deterministic Finite Automata (DFA) constructed from regular expressions. It delves into the subset construction method used to derive DFAs from regular expressions containing characters 'a', 'b', and 'c'. The final states resulting from this conversion are then subjected to a minimization algorithm to produce an equivalent minimal DFA. The study highlights the importance of optimizing automata for efficiency in computational tasks, demonstrating practical application through examples and formal definitions.

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Minimization of DFA with Subset Construction for Regular Expressions

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  1. a+b  a b b q0 q1 q2 q3 q4 Motsvarande RE = ( a+b )* abb

  2. a a a b b s0 s1 s3 s4 a b a b s2 b DFA för ( a + b )*abb

  3. a a a b b s0 s1 s3 s4 a b a b s2 b b a a a b b s0 , s2 s1 s3 s4 a b Minimering av DFA sluttillstånd

  4. b q5 q4   a    q0 q1 q2 q3 q9 q8 c   q7 q6  Final states DFA Minimization a ( b + c )* The subset construction b s2 b a s0 s1 b c c s3 c

  5. b s2 b + c b a s0 s1 a b c s0 s1 c s3 c Then, apply the minimization algorithm to produce the minimal DFA final states

  6. A B C D E

  7. q 0

  8. b b a b a q0 q1 q2 a

  9. b b a b a q0 q1 q2 a

  10. 1 2 3 4 5 6

  11. Ratio(x,2)

  12. Greater?

  13. Sipser 2.10 p. 105

  14. 1 2 3 4 5

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