Automata Theory: Finite Automaton Models

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Questions and Answers

What is a finite automaton used for?

  • Recognizing patterns in input (correct)
  • Creating new programming languages
  • Simulating real-world environments
  • Performing complex computations

How many states do finite automata typically have?

  • Twenty
  • Five
  • Ten
  • Two (correct)

What is the purpose of the transition function in a finite automaton?

  • Storing input symbols
  • Performing calculations
  • Displaying output
  • Deciding the next state based on input (correct)

Which component of a finite automaton represents the initial state?

<p>q0 (B)</p>
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What does the finite control of a finite automaton do?

<p>Decides the next state based on input tape symbols (D)</p>
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In the context of finite automata, what does the term 'quintuple' refer to?

<p>(a, ∑,q0, δ,F) (B)</p>
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What is a key difference between DFA and NFA?

<p>DFA is used in Lexical Analysis, while NFA is more theoretical. (C)</p>
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In a finite automaton, what do the states (Q) represent?

<p>The set of possible configurations the automaton can be in. (C)</p>
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Which of the following conventions is typically used to represent input symbols in automata?

<p>a, b, c: input symbols (C)</p>
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What does the set F represent in a finite automaton?

<p>The final state(s). (D)</p>
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Which of the following statements is true regarding DFA and NFA?

<p>NFA can have multiple final states, but DFA cannot. (B)</p>
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What role does the transition table play in a finite-state automaton?

<p>It specifies the state transitions based on input symbols. (C)</p>
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Flashcards

What is a finite automaton used for?

Recognizing patterns in input.

Transition function in a finite automaton.

Deciding the next state based on input.

q0 represents what?

The initial state.

Finite control of a finite automaton.

Decides the next state based on input tape symbols.

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What does the term 'quintuple' in automata refer to?

The components of a finite automaton: states, alphabet, initial state, transition function, and final states.

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DFA and NFA key difference?

DFA is used in Lexical Analysis, while NFA is more theoretical.

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States (Q) represent what?

The set of possible configurations the automaton can be in.

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Input symbols in automata.

a, b, c represent input symbols.

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What does the set F represent?

The final state(s).

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DFA and NFA statement.

NFA can have multiple final states, but DFA cannot.

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Transition table role.

Specifies the state transitions based on input symbols.

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Study Notes

Finite Automaton

  • A finite automaton is a mathematical model of a simple idealized machine used to recognize patterns within input taken from some character set (or alphabet).

Finite State System

  • A finite state system defines an infinite language with a set of strings labeled from the initial state to the final state.

Finite Automata

  • Finite automata recognize patterns by taking a string of symbols as input and changing its state accordingly.
  • When the desired symbol is found, a transition occurs, and the automaton can either move to the next state or stay in the same state.
  • Finite automata have two states: Accept state or Reject state.

Formal Definition

  • A finite automaton can be formally defined as a quintuple M = (Q, ∑, q0, δ, F), where:
    • Q: finite set of states
    • ∑: finite set of input symbols
    • q0: initial state
    • F: final state
    • δ: transition function

Finite Automata Model

  • A finite automaton can be represented by an input tape and finite control.
  • The input tape is a linear tape with cells, each containing an input symbol.
  • The finite control decides the next state based on the input from the input tape.

Types of Automata

  • There are two types of finite automata: DFA (Deterministic Finite Automata) and NFA (Non-Deterministic Finite Automata).

DFA and NFA

  • Every DFA is an NFA, but not every NFA is a DFA.
  • Both DFA and NFA can have multiple final states.
  • DFA is used in Lexical Analysis in Compiler, while NFA is more of a theoretical concept.

Symbols Used

  • State: represents a state in the finite automaton
  • Final State label: represents the final state of the finite automaton
  • Initial State: represents the initial state of the finite automaton

Transition mark

  • Transition mark: represents the transition from one state to another based on input symbols.

Conventions

  • 0, 1, a, b, c : input symbols
  • w, x, y : strings
  • q, p : states
  • ε : null string

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