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GATE 2015 CS (CS3) – Question 32

Theory of Computation · Regular Expressions and Finite Automata · 1 mark · Multiple choice

Over Σ={0,1}, let L be represented by Σ*0011Σ*. Find the minimum DFA-state count for its complement.

  1. 4
  2. 5
  3. 6
  4. 8

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Correct answer: (B) 5

Explanation

A DFA detecting substring 0011 needs states for matched prefixes ε,0,00,001, plus an absorbing “found” state, five total. These are distinguishable by completion suffixes. Complementing a complete DFA exchanges accepting states and preserves distinguishability, so the complement also needs five states, B.

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