Formal Language Theory Quiz
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Questions and Answers

Which of the following best describes the relationship between a character and a symbol?

  • A symbol is a specific type of character.
  • Characters and symbols represent different concepts with no connection.
  • A character is a specific type of symbol. (correct)
  • Characters and symbols are interchangeable terms.

    • What is the correct order of the Chomsky hierarchy classes from smallest to largest?

  • Type 1, Type 2, Type 3, Type 0
  • Type 0, Type 1, Type 2, Type 3
  • Type 2, Type 3, Type 0, Type 1
  • Type 3, Type 2, Type 1, Type 0 (correct)

    • Which type of automata is associated with Context-Free Languages?

  • Pushdown Automata (correct)
  • Turing Machine
  • Linear Bounded Automata
  • Finite Automata

    • If Σ = {a, b}, what is the result of Σ^2?

    <p>{aa, ab, ba, bb}</p> Signup and view all the answers

    What is the defining characteristic of a language in the context of formal language theory?

    <p>It is a subset of Σ*.</p> Signup and view all the answers

    What is the relationship between a token and a string?

    <p>A token is a specific instance of a string.</p> Signup and view all the answers

    Which of the following is NOT a type of language in the Chomsky hierarchy?

    <p>Procedural Language</p> Signup and view all the answers

    What does Σ* represent?

    <p>The set of all possible strings over an alphabet.</p> Signup and view all the answers

    If every state in a DFA is non-final, what is the language recognized by that DFA?

    <p>The empty set, denoted as ∅ or {}</p> Signup and view all the answers

    Given a language L, which of the following is true about L and its complement L?

    <p>L ∪ L = Σ* and L ∩ L = ∅</p> Signup and view all the answers

    What is the minimum number of states required in a DFA to recognize a language where all strings have length equal to n or less than or equal to n?

    <p>n + 2 states</p> Signup and view all the answers

    What is the minimum number of states required in a minimum DFA, that accepts the language consisting of strings over alphabet {a, b}, where the number of 'a's is divisible by m and the number of 'b's is divisible by n?

    <p>m * n states</p> Signup and view all the answers

    Consider a language where the nth symbol of every string (from the beginning) over the alphabet {a, b} is 'a'. What is the number of states needed in the minimal DFA?

    <p>n + 2 states</p> Signup and view all the answers

    Which statement is true concerning the relationship between DFAs and NFAs for a given regular language?

    <p>For every regular language, there exists only one unique minimum DFA.</p> Signup and view all the answers

    If a language requires that the nth symbol from the start of any string over alphabet {a,b} is 'a', how many states are needed in the minimum NFA?

    <p>n + 1 states</p> Signup and view all the answers

    How does the minimum number of states needed for a DFA differ for strings of length |w| = n and |w| ≥ n?

    <p>The first requires n+2 and the second requires n+1 states.</p> Signup and view all the answers

    According to the given rules, what is the result of the operation a + ∅?

    <p>a</p> Signup and view all the answers

    What is the result of the Kleene closure operation applied to the empty set, ∅*?

    <p>∈</p> Signup and view all the answers

    Which of the following is a correct representation of a positive closure, 'R⁺'?

    <p>R¹ + R² + R³ + ...</p> Signup and view all the answers

    Which of these operations result in a?

    <p>a ∙ ∈</p> Signup and view all the answers

    According to provided properties, is concatenation commutative?

    <p>No</p> Signup and view all the answers

    Given the language L = {aⁿbᵐ | n, m ≥ 0}, which of the following is the correct regular expression?

    <p>a<em>b</em></p> Signup and view all the answers

    What is the equivalent regular set for ∈ + ∈?

    <p>{∈}</p> Signup and view all the answers

    Based on the provided properties, which expression acts as an annihilator for concatenation?

    <p>∅</p> Signup and view all the answers

    What is the key difference between the transition functions of a Nondeterministic Finite Automaton (NFA) and a Deterministic Finite Automaton (DFA)?

    <p>NFA uses a transition function $Q \times \Sigma \rightarrow 2^Q$, while DFA uses $Q \times \Sigma \rightarrow Q$.</p> Signup and view all the answers

    Consider a language where all strings have a length of exactly $n$ over the alphabet {a, b}. How many states are required in a minimal DFA and NFA?

    <p>DFA: $n+2$, NFA: $n+1$</p> Signup and view all the answers

    For a language where the $n^{th}$ symbol from the end of any string is ‘a’, what is the number of states in the minimum DFA and NFA, respectively?

    <p>DFA: $2n$, NFA: $n+1$</p> Signup and view all the answers

    How does the number of states in a DFA relate to the number of states in an equivalent NFA, and what process do we apply to achieve this?

    <p>A NFA with n states results in a DFA with at most $2^n$ states, using the subset construction method.</p> Signup and view all the answers

    Which of the following is true regarding paths for valid and invalid strings in an NFA?

    <p>Valid strings have one path, and invalid strings have zero or more paths.</p> Signup and view all the answers

    Which description accurately reflects the relationship between Moore and Mealy machines?

    <p>In Moore machines, output is associated with states, while in Mealy machines, output is associated with transitions.</p> Signup and view all the answers

    Given the language {w | w ∈ {a, b}*, |w| ≥ n}, how many states are required for a minimal NFA and DFA respectively?

    <p>NFA: n+1, DFA: n+2</p> Signup and view all the answers

    Which statement is correct about the interrelation of different Finite Automata (FA)?

    <p>Every DFA is an NFA, but not every NFA is a DFA.</p> Signup and view all the answers

    Which of the following languages is considered a regular language?

    <p>L = {a*} over Σ = {a}</p> Signup and view all the answers

    Which language is NOT a regular language?

    <p>L = { anbn | n &gt;= 0}</p> Signup and view all the answers

    Which of these languages is described as a non-regular language?

    <p>L = {a^2 | n &gt; 0} over Σ = {a}</p> Signup and view all the answers

    The language L = {a^n! | n >= 100} is classified as what type of language?

    <p>Non-regular language</p> Signup and view all the answers

    Which of the following languages is a regular language?

    <p>L = {a2n |n &gt;= 0}</p> Signup and view all the answers

    Which language is classified as a DCFL (Deterministic Context-Free Language)?

    <p>L = { ambnc* | c &lt;= n }</p> Signup and view all the answers

    Which language is NOT a Context-Free Language (CFL)?

    <p>All of the above are CFLs</p> Signup and view all the answers

    Given the language L = {aPrime}*, how would it be categorized?

    <p>Regular language</p> Signup and view all the answers

    Which of the following is NOT equivalent to a standard Turing Machine (TM)?

    <p>Finite Automata with one stack</p> Signup and view all the answers

    If a Turing Machine always halts, and uses a linearly bounded tape, what type of language does it accept?

    <p>Context-Sensitive Language</p> Signup and view all the answers

    What is the key difference between a Deterministic Turing Machine (DTM) and a Non-Deterministic Turing Machine (NTM) based on their transition functions?

    <p>DTM transitions are always to a single state whereas NTM can be to multiple states.</p> Signup and view all the answers

    What is another name for Unrestricted Grammar (UG)?

    <p>Phase structure grammar</p> Signup and view all the answers

    Which of the following is true about Left Linear Grammar (LLG)?

    <p>It has the form V → V T* | T*</p> Signup and view all the answers

    Which of the following describes a Turing Machine that always halts?

    <p>It is a Halting Turing Machine (HTM).</p> Signup and view all the answers

    A Turing Machine (TM) with what specific restriction will only accept regular languages?

    <p>The TM tape is read-only and the head is unidirectional</p> Signup and view all the answers

    What type of language is accepted by a Linear Bounded Automaton (LBA)?

    <p>Context-Sensitive languages</p> Signup and view all the answers

    Study Notes

    Theory of Computation

    • This subject matter involves the study of computation, languages, and automata.
    • It deals with the limitations and capabilities of computers.

    Index

    • Basics of Theory of Computation: Sections 7.1-7.5
    • Finite Automata: Sections 7.6-7.21
    • Push Down Automata: Sections 7.22-7.29
    • Turning Machine: Sections 7.30-7.39

    Basics of Theory of Computation

    • Symbol: A unique, indivisible unit.
    • Alphabet: A finite set of symbols. Examples include the English alphabet (a-z), binary alphabet (0, 1), decimal alphabet (0-9).
    • String: A sequence of symbols defined over an alphabet. Strings over alphabets can be empty (null), one character (length 1), or more complex (variable length). Examples are English words, binary sequences, or decimal numbers.
    • Operations on Strings:
      • Length: The number of symbols in a string. For a string 'w', the length is |w|.
      • Reversal: The reverse order of symbols. If 'w' = 'abb', then 'wR' = 'bba'.
      • Concatenation: Joining two strings together. If 'w1' = 'a' and 'w2' = 'ba', then 'w1w2' = 'aba'.
      • Prefixes: A substring that starts at the beginning of a string (including the empty string).
      • Suffixes: A substring that ends at the end of a string (including the empty string).
      • Substrings: Any contiguous sequence of symbols within a string.

    Finite Automata

    • Finite Automata (FA): Describes or represents a regular language. Two types exist:
      • Acceptor: Accepts or rejects given input strings.
      • Transducer: Produces output strings for given input strings.
    • Finite Automata (FA) components:
      • Set of states (Q)
      • Alphabet (Σ)
      • Transition function
      • Initial state (q0)
      • Set of final states (F)

    Push Down Automata

    • Push-down Automata is a type of Finite Automata (FA) that accepts Context Free Languages.

    Turing Machine

    • Turing Machine is a type of Finite Automata that accepts recursively enumerable languages.
    • Turing Machines have components:
      • States (Q)
      • Input alphabet (Σ)
      • Tape alphabet (Γ)
      • Transition function
      • Start state (q0)
      • Final state(s)
    • There are two types of Turing Machines:
      • Deterministic Turing Machines (DTM)
      • Non-Deterministic Turing Machines (NDTM)

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    Theory of Computation PDF

    Description

    Test your understanding of formal language theory with this quiz that covers concepts from the Chomsky hierarchy to automata theory. Challenge yourself with questions about symbols, tokens, and various types of languages. Perfect for students of computer science and linguistics!

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