4110 Exam 2 Weber State

1-15 Module 5. 16-53 Module 6

What are the three key elements of a Context-Free Grammar (CFG)?

 

Terminals, productions, start symbol

 

Terminals, nonterminals, productions

 

Terminals, nonterminals, language

 

Productions, nonterminals, start symbol

Terminals, nonterminals, productions

What is the number of production rules needed to construct a CFG defining the language represented by a FA with four states, including one start state, one final state, and two other states?

 

4

 

8

 

9

 

10

9

For a FA with n states converted to a CFG, you get one production per transition plus one extra production per final state (adding Λ). With 4 states and some transitions, the standard result for this configuration is 9 rules.

Find all nullable nonterminals in the given Context-Free Grammar: S -> AB; A -> Λ; B -> C; C -> a | Λ. 

 

A and C

 

A and B

 

A, B, and C

 

A, B, C, and S

A, B, C, and S

What is the primary purpose of eliminating unit productions in a context-free grammar?

 

To reduce the overall size of the grammar.

 

To simplify the grammar by removing nonterminal symbols.

 

To improve parsing efficiency and avoid any unnecessary derivations.

 

To enhance the expressiveness of the language generated by the grammar.

To improve parsing efficiency and avoid any unnecessary derivations.

In context-free grammars, what is a key characteristic of Chomsky Normal Form (CNF)?

 

CNF allows the use of regular expressions in productions.

 

CNF mandates that all productions must have the form A -> BC or A -> a.

 

CNF requires the use of left-recursion in productions for enhanced expressiveness.

 

CNF permits the use of ambiguous productions to increase language complexity.

CNF mandates that all productions must have the form A -> BC or A -> a.

Which statement accurately describes a leftmost derivation in the context of context-free grammars?

 

A leftmost derivation always starts with the rightmost nonterminal and expands towards the left.

 

A leftmost derivation always begins with the leftmost nonterminal and expands it first in each step.

 

A leftmost derivation is a process where productions are applied randomly to any nonterminal in each step.

 

A leftmost derivation exclusively focuses on terminal symbols and ignores nonterminals.

A leftmost derivation always begins with the leftmost nonterminal and expands it first in each step.

Question 1

1 / 1 pts

What is the language generated by a CFG that includes terminals ‘a’ and ‘b’ and productions S -> aS, S -> bS, S -> a, S -> b?

 

Set of all possible strings of symbols

 

Set of all strings of nonterminals only

 

Set of all strings of terminals only

 

Set of all strings of the letters ‘a’ and ‘b’

Set of all strings of the letters ‘a’ and ‘b’

What does the start symbol in a CFG guide?

 

The substitution process

 

The parsing process

 

The generation process

 

The programming process

The generation process

In a CFG with productions S -> SS, S -> a, S -> Λ, how is the word ‘aa’ derived?

 

S => aS => aSa => aSaa => aSaaa => aaaa

 

S => aS => aaS => aaaS => aaaaS => aaaaaS => aaaaaaS => aaaaaa => aaaaaaΛ

 

S -> SS -> SSS -> SaS -> SaSS -> ΛaSS -> ΛaaS -> ΛaaΛ -> aa

 

S => SS => SSS => SaS => SaSS => ΛaSS => ΛaaS => ΛaaΛ => aa

S => SS => SSS => SaS => SaSS => ΛaSS => ΛaaS => ΛaaΛ => aa

In a Context-Free Grammar (CFG), what do Nonterminal -> Semiword productions represent?

 

Concluding the CFG generation

 

Generating strings consisting solely of terminals

 

Expanding nonterminals into semiwords

 

Initiating the CFG construction

Expanding nonterminals into semiwords

What is the first crucial step in the constructive algorithm to derive a CFG from an FA?

 

Identifying nonterminals

 

Initiating the CFG construction

 

Creating Final State Productions

 

Crafting Edge-Based Productions

Identifying nonterminals

What does Theorem 21 state about the relationship between Finite Automata (FA) and Context-Free Grammars (CFG)?

 

FAs and CFGs are unrelated

 

For any FA, there is a CFG generating the same language

 

CFGs cannot generate languages accepted by FAs

 

FAs are a subset of CFGs

For any FA, there is a CFG generating the same language

The theorem 23 states that if a CFG includes null-productions, an alternative CFG can be devised that:

 

Does not have any null-productions

 

Introduces more ambiguity

 

Limits the language’s complexity

 

Reduces the expressive power

Does not have any null-productions

How does the process of eliminating unit productions contribute to simplifying context-free grammars?

 

Increased Complexity

 

Reduction of Unnecessary Derivations

 

Indirect Representations

 

Mandatory use of unit productions

Reduction of Unnecessary Derivations

Given the following context-free grammars (CFGs), which one is in Chomsky Normal Form (CNF)?

 

S → AB | BC; A → a; B → b; C → AB | S | BS

 

S → AC | BA; A → a | b; B → S; C → AB | b

 

S → AB | BC; A → a | Λ; B → CC | b; C → AB | a

 

S → aB | bA; A → aS | b; B → bS | a

S → AC | BA; A → a | b; B → S; C → AB | b

In a pushdown automaton, if the machine pushes A, then B, then S onto the stack, and performs two pop operations, what remains on the top of the stack?

 

A

 

B

 

S

 

Empty Symbol

A

In Theorem 30, a constructive algorithm is employed to construct a PDA from a given CFG. Which of the following conditions must be satisfied to execute this process?

 

The CFG must be a regular grammar.

 

The CFG must be in Chomsky Normal Form.

 

The CFG must consist of a single nonterminal symbol.

 

The CFG must produce finite number of words.

The CFG must be in Chomsky Normal Form.

A context-free grammar (CFG) has 7 live productions and 3 dead productions. If we apply 11 live productions to generate a word, how many dead productions are required to produce the word?

 

8

 

10

 

12

 

14

12

Language L1 is PALINDROME and language L2 is aⁿbⁿ, n = 1, 2, 3, ..., which of the following strings is in the language L1L2?

 

abba

 

bbabbaabb

 

aaabbbaaa

 

aabb

bbabbaabb

L1 = bbabb - palindrome
L2 = aabb - a^n b^n

What does the READ state represent in the enhanced Finite Automata (FA) diagrams?

 

Popping the top of the stack.

 

Accepting the input string.

 

Transition to the next state.

 

Consuming the next input symbol.

Consuming the next input symbol.

What is the purpose of the INPUT TAPE in context with Pushdown Automata (PDAs)?

 

To use as memory of the machine.

 

To store the input string for processing.

 

To limit the length of input.

 

To create randomness in transitions.

To store the input string for processing.

What element is introduced to augment the capabilities of Finite Automata (FAs) in understanding context-free languages?

 

Output buffer

 

Input tape

 

Input buffer

 

Output tape

Input tape

Which of the following is true?

 

Every context-free language is also a regular language.

 

For every language generated by a CFG, there exists a corresponding PDA that recognizes the same language.

 

Every context-free language can be recognized by a finite automaton.

 

For every PDA, there exists a corresponding regular expression that generates the same language.

For every language generated by a CFG, there exists a corresponding PDA that recognizes the same language.

What is the purpose of simulating leftmost derivations in the PDA construction?

 

To verify the correctness of the CFG

 

To test the PDA’s computational power

 

To demonstrate the versatility of PDAs

 

To ensure recognition of all generated words

To ensure recognition of all generated words

In the theorem regarding self-embedded nonterminals, what happens if the length of the word w is more than 2P, where P represents the number of live productions?

 

No nonterminals repeat themselves

 

The theorem is disproven

 

Nonterminals repeat themselves in the production tree

 

The production tree becomes a binary tree.

Nonterminals repeat themselves in the production tree

What role do production trees play in understanding language construction?

 

To showcase artistic tree drawings

 

To categorize different types of trees

 

To illuminate the pathways of language construction

 

To navigate physical trees in forests

To illuminate the pathways of language construction

How does the Pumping Lemma help analyze context-free languages?

 

It determines the computational complexity of PDAs.

 

It establishes the hierarchy of nonterminals.

 

It identifies patterns within words generated by CFGs.

 

It defines the syntax of regular languages.

It identifies patterns within words generated by CFGs.

What modification is made to the original start symbol in the construction of a grammar for the Kleene star of a language?

 

It is appended with a subscript.

 

It is removed from the grammar.

 

It is converted into a terminal symbol.

 

It is replaced by a new symbol.

It is appended with a subscript.

According to Theorem 38, what is the relationship between a context-free language (L) and its Kleene star (L*)?

 

L* is equivalent to L.

 

If L is a CFL, then L* is also a CFL.

 

L* is a subset of L.

 

L is a subset of L*.

If L is a CFL, then L* is also a CFL.

What is the significance of a POP operation in a PUSHDOWN STACK?

 

Removing the top letter from the stack

 

Reversing the stack

 

Erasing the entire stack

 

Adding a new letter to the top of the stack

Removing the top letter from the stack

What is the significance of a PUSH operation in a PUSHDOWN STACK?

 

Reversing the stack

 

Adding a new letter to the top of the stack

 

Erasing the entire stack

 

Popping the top letter

Adding a new letter to the top of the stack

What kind of machine is equivalent to Context-Free Grammars (CFGs)?

 

Deterministic Pushdown Automata (DPDA)

 

Nondeterministic Pushdown Automata (NPDA)

 

Regular Expressions (RE)

 

Nondeterministic Finite Automata (NFA)

Nondeterministic Pushdown Automata (NPDA)

What is the primary purpose of the stack in a PDA?

 

To store input symbols

 

To store terminals

 

To facilitate recognizing languages beyond finite automata

 

To store nonterminals

To facilitate recognizing languages beyond finite automata

How are terminal productions represented in the transition diagram of a PDA?

 

a START and a “PUSH S“ state

 

a loop with two PUSH states

 

a circuit with the central POP and a read state

 

a POP-READ-ACCEPT path

a circuit with the central POP and a read state

What is the significance of the production tree in context-free grammars?

 

It controls the order of productions.

 

It defines the syntax of the language.

 

It organizes the terminals and nonterminals.

 

It illustrates the derivation process of a word.

It illustrates the derivation process of a word.

According to Theorem 32, what is the relationship between the length of a word and the number of live productions in a CNF grammar?

 

The length of the word is limited by the number of live productions.

 

The length of the word is unlimited.

 

The number of live productions depends on the length of the word.

 

They are inversely proportional.

The length of the word is limited by the number of live productions.

How is a self-embedded nonterminal defined in Theorem 32?

 

A nonterminal that occurs as a descendant of itself within a production tree

 

A nonterminal that cannot be derived from other nonterminals

 

A nonterminal that repeats only once in a production tree

 

A nonterminal that is replaced by a terminal symbol

A nonterminal that occurs as a descendant of itself within a production tree

How is the construction of a grammar for L* achieved according to Theorem 38?

 

By introducing a new start symbol and a production rule allowing for repetition or an empty word.

 

By converting all production rules into regular expressions.

 

By removing all nonterminal symbols from the original grammar.

 

By adding a suffix to each terminal symbol in the original grammar.

By introducing a new start symbol and a production rule allowing for repetition or an empty word.

What type of states in Finite Automata (FA) are also referred to as “halt states”?

Group of answer choices

Initial states

Intermediate states

Transition states

Accept and Reject states

Accept and Reject states

What is the purpose of simulating leftmost derivations in the PDA construction?

 

To demonstrate the versatility of PDAs

 

To test the PDA’s computational power

 

To verify the correctness of the CFG

 

To ensure recognition of all generated words

To ensure recognition of all generated words

A CFG has 8 live productions and 5 dead productions. Words generated by this CFG without reusing live productions can have at most how many letters?

 

9

 

6

 

5

 

8

9

What distinguishes live productions from dead productions in a context-free grammar (CFG)?

 

Dead productions increase the count of nonterminals

 

Live productions increase the count of nonterminals

 

Dead productions decrease the count of terminals

 

Live productions increase the count of terminals

Live productions increase the count of nonterminals

Will the union of three context-free languages (CFLs) remain a context-free language?

 

It depends on the specific languages being combined

 

Yes, always

 

No, never

 

Only if the languages are regular

Yes, always

Which operation preserves the context-free property of languages?

 

Reversion

 

Union

 

Complementation

 

Intersection

Union

In constructing a PDA from a CFG, which of the following is needed?

 

Assume the CFG is in CNF

 

Add a new start symbol

 

Add a stack to store the input

 

Create a finite automaton

Assume the CFG is in CNF

What is the requirement for a word w in Theorem 33 to have a self-embedded nonterminal?

 

The length of w must exceed 2p where p is the number of live productions.

 

The length of w must be equal to the number of live productions.

 

The length of w must exceed twice the number of live productions.

 

The length of w must be less than the number of live productions.

The length of w must exceed 2p where p is the number of live productions.

What role do “u”, “v”, “x”, “y”, and “z” play in the Pumping Lemma for context-free languages?

 

They indicate the number of live productions.

 

They partition a word to demonstrate a repeated pattern.

 

They define the length of a word.

 

They represent terminals in a production tree.

They partition a word to demonstrate a repeated pattern.

How does the construction of a grammar for the product language differ from that of the combined language?

 

The combined language utilizes a different production rule for generating words.

 

The product language uses a different set of terminal symbols.

 

The product language involves concatenation of words from two languages.

 

The combined language employs a different start symbol.

The product language involves concatenation of words from two languages.

According to the connection between context-free languages and PDAs, what is true?

 

PDAs cannot recognize context-free languages.

 

PDAs are only equivalent to regular languages.

 

For each context-free language, there exists a corresponding nondeterministic PDA.

 

For each context-free language, there is no corresponding PDA.

For each context-free language, there exists a corresponding nondeterministic PDA.

Which of the following statements best describes a Pushdown Automaton (PDA)?

 

It consists of only two states for recognizing regular languages.

 

It includes a stack for recognizing languages beyond finite automata.

 

It has no memory, unlike a Finite Automaton.

 

It recognizes languages with infinite alphabets.

It includes a stack for recognizing languages beyond finite automata.

How are nonterminal productions represented in the transition diagram of a PDA?

 

a START and a “PUSH S“ state

 

a POP-READ-ACCEPT path

 

a loop with two PUSH states

 

a circuit with the central POP and a read state

a loop with two PUSH states

What is the purpose of adding a new start symbol and a production rule “S -> S1 | S2” in the construction of the combined grammar for L1 + L2?

 

To combine words from L1 and L2 seamlessly.

 

To remove ambiguity from the grammar.

 

To create a recursive structure in the grammar.

 

To generate new nonterminal symbols.

To combine words from L1 and L2 seamlessly.