Nondeterminism in Theory of Computation
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Questions and Answers

What happens when a multiple-copy machine encounters a symbol that doesn't appear on any of the existing arrows?

  • That copy of the machine dies. (correct)
  • It splits into more copies.
  • It moves to an accept state.
  • It stays in the same state.

    • When an NFA is in an accept state at the end of the input, what does it mean?

  • The NFA stays in the same state.
  • The NFA rejects the input string.
  • The NFA dies.
  • The NFA accepts the input string. (correct)

    • What happens when an € symbol is encountered on an existing arrow?

  • The machine dies.
  • The machine stays in the same state.
  • The machine moves to an accept state.
  • The machine splits into multiple copies. (correct)

    • What is the primary difference between a DFA and an NFA?

    <p>A DFA is deterministic, while an NFA is nondeterministic.</p> Signup and view all the answers

    What is the purpose of an NFA?

    <p>To recognize a specific language.</p> Signup and view all the answers

    Study Notes

    Nondeterminism

    • Nondeterminism is a concept that has had a great impact on the theory of computation.
    • In a nondeterministic machine, several choices may exist for the next state at any point.
    • Nondeterminism is a generalization of determinism, so every deterministic finite automaton is automatically a nondeterministic finite automaton.

    Nondeterministic Finite Automata (NFA)

    • An NFA may have additional features compared to a deterministic finite automaton (DFA).
    • In an NFA, a state may have zero, one, or many exiting arrows for each alphabet symbol.
    • An NFA may have arrows labeled with members of the alphabet or ε.
    • Zero, one, or many arrows may exit from each state with the label ε.

    How does an NFA compute?

    • When running an NFA on an input string and coming to a state with multiple ways to proceed, the machine splits into multiple copies of itself and follows all the possibilities in parallel.
    • If there are subsequent choices, the machine splits again.
    • If a copy of the machine is in an accept state at the end of the input, the NFA accepts the input string.
    • If an ε symbol is occurring on an existing arrow, the machine splits into multiple copies, one following each of the exiting ε-labeled arrows, and one staying at the current state.

    Example NFA

    • The NFA N1 recognizes the language consisting of all strings over {0,1} containing a 1 in the third position from the end.
    • The NFA N2 recognizes the language A, which consists of all strings over {0,1} containing a 1 in the third position from the end.
    • The NFA can be converted into an equivalent DFA, but the DFA may have many more states.

    Converting NFA to DFA

    • Converting an NFA into an equivalent DFA may result in a DFA with many more states.
    • The procedure for converting NFA to DFA will be illustrated later.

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    Description

    This quiz covers the concept of nondeterminism in Theory of Computation, specifically in the context of Finite Automata. It explores how nondeterminism impacts the computation process.

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