`tell me the concept of Deterministic Finite Automata`

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Answer from Sia

Posted 3 months ago

Deterministic Finite Automata (DFA) is a theoretical model of computation used in computer science to represent and manipulate a set of strings.

A DFA is defined by a 5-tuple $(Q, \Sigma, \delta, q_0, F)$ where:

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$Q$ : is a finite set of states

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$\Sigma$ : is a finite set of input symbols (alphabet)

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$\delta$ : is the transition function, $\delta: Q \times \Sigma \rightarrow Q$

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$q_0$ : is the start state, where $q_0 \in Q$

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$F$ : is the set of accept states, where $F \subseteq Q$

The DFA operates by reading a string of symbols from the input alphabet $\Sigma$ and transitioning between states according to the transition function $\delta$. If the DFA ends in an accept state after reading the entire input string, the string is accepted; otherwise, it is rejected.

Here is an example of a DFA with the following components:

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$Q = \{q_0, q_1, q_2\}$

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$\Sigma = \{0, 1\}$

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$\delta$ defined as:

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$\delta(q_0, 0) = q_1$

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$\delta(q_0, 1) = q_0$

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$\delta(q_1, 0) = q_2$

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$\delta(q_1, 1) = q_0$

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$\delta(q_2, 0) = q_2$

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$\delta(q_2, 1) = q_2$

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$q_0$ is the start state

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$F = \{q_2\}$

The LaTeX code to generate the graph of this DFA is as follows:

latex

This code will generate a visual representation of the DFA with states $q_0$, $q_1$, and $q_2$, and the transitions as defined above.

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