Which of the following problems is undecidable ?

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UGC NET Computer Science (Paper 3) Nov 2017 Official Paper
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  1. To determine if two finite automata are equivalent
  2. Membership problem for context free grammar
  3. Finiteness problem for finite automata
  4. Ambiguity problem for context free grammar

Answer (Detailed Solution Below)

Option 4 : Ambiguity problem for context free grammar
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The correct answer is option 4:

EXPLANATION

Option 1: Decidable

Minimize both finite automata if both are the same having automata then both are equivalent and hence to determine if two finite automata are equivalent is decidable 

Option 2: Decidable

For the context-free language, we have a CYK algorithm for membership problem, so it is decidable

Option 3: Decidable

There is an algorithm for the finiteness problem

ALGORITHM:

Step1: delete states which are not reachable from the initial state and corresponding transitions.

Step 2: delete states and corresponding transitions which are not reachable to the final state.

Step 3: In remaining finite automata, if we find at least one loop and one final state then it is accepting infinite language.

so the finiteness problem is decidable

Option 4: Undecidable

Decidable there is no algorithm for finding ambiguity in grammar, so ambiguity is undecidable.

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