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Non Deterministic Automata

This article explores the concept of Nondeterministic Finite Acceptors (NFA), explaining their structure and functioning. An NFA accepts a string if a computation exists that leads to acceptance, even with multiple possible transitions for the input alphabet. The discussion includes key examples demonstrating how strings are accepted or rejected in NFAs, particularly highlighting lambda transitions where the read head does not move. Additionally, it offers a formal definition covering states, input alphabet, transition functions, and acceptance criteria.

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Non Deterministic Automata

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  1. Non Deterministic Automata

  2. Nondeterministic Finite Accepter (NFA) Alphabet =

  3. Nondeterministic Finite Accepter (NFA) Alphabet = Two choices

  4. Nondeterministic Finite Accepter (NFA) Alphabet = Two choices No transition No transition

  5. First Choice

  6. First Choice

  7. First Choice

  8. First Choice “accept”

  9. Second Choice

  10. Second Choice

  11. Second Choice No transition: the automaton hangs

  12. Second Choice “reject”

  13. Observation An NFA accepts a string if there is a computation of the NFA that accepts the string

  14. Example is accepted by the NFA:

  15. Lambda Transitions

  16. (read head doesn’t move)

  17. “accept” String is accepted

  18. Language accepted:

  19. Another NFA Example

  20. “accept”

  21. Another String

  22. “accept”

  23. Language accepted

  24. Another NFA Example

  25. Language accepted

  26. Formal Definition of NFAs Set of states, i.e. Input aplhabet, i.e. Transition function Initial state Final states

  27. Transition Function

  28. Extended Transition Function

  29. Formally It holds if and only if there is a walk from to with label

  30. The Language of an NFA

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