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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?
When an NFA is in an accept state at the end of the input, what does it mean?
What happens when an € symbol is encountered on an existing arrow?
What is the primary difference between a DFA and an NFA?
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What is the purpose of an NFA?
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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.
