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Decidable Problems of Regular Languages

Decidable Problems of Regular Languages. Answer:. Take the DFA that accepts and check if is accepted. Membership Question. Question:. Given regular language and string how can we check if ?. DFA. DFA. Question:. Given regular language how can we check

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Decidable Problems of Regular Languages

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  1. Decidable ProblemsofRegular Languages Prof. Busch - RPI

  2. Answer: Take the DFA that accepts and check if is accepted Membership Question Question: Given regular language and string how can we check if ? Prof. Busch - RPI

  3. DFA DFA Prof. Busch - RPI

  4. Question: Given regular language how can we check if is empty: ? Answer: Take the DFA that accepts Check if there is any path from the initial state to an accepting state Prof. Busch - RPI

  5. DFA DFA Prof. Busch - RPI

  6. Question: Given regular language how can we check if is finite? Answer: Take the DFA that accepts Check if there is a walk with cycle from the initial state to a final state Prof. Busch - RPI

  7. DFA is infinite DFA is finite Prof. Busch - RPI

  8. Answer: Find if Question: Given regular languages and how can we check if ? Prof. Busch - RPI

  9. and Prof. Busch - RPI

  10. or Prof. Busch - RPI

  11. Decidable Problemsof Context-Free Languages Prof. Busch - RPI

  12. Parsers Membership Algorithms: • Exhaustive search parser • CYK parsing algorithm Membership Question: for context-free grammar find if string Prof. Busch - RPI

  13. Algorithm: • Remove useless variables • Check if start variable is useless Empty Language Question: for context-free grammar find if Prof. Busch - RPI

  14. Infinite Language Question: Algorithm: 1. Remove useless variables 2. Remove unit and productions 3. Create dependency graph for variables 4. If there is a loop in the dependency graph then the language is infinite for context-free grammar find if is infinite Prof. Busch - RPI

  15. Example: Infinite language Dependency graph Prof. Busch - RPI

  16. Prof. Busch - RPI

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