40 Lecture - Conversion form of PDA

  1. Home
  2. Courses
  3. Theory of Automata
  4. 40 Lecture

40 Lecture

CS402

Midterm & Final Term Short Notes

Conversion form of PDA

The conversion from a Context-Free Grammar (CFG) to a Pushdown Automaton (PDA) involves constructing a PDA that can recognize the same language as the CFG. This process involves creating a PDA that can push and pop symbols onto a stack and trans


Important Mcq's
Midterm & Finalterm Prepration
Past papers included

Download PDF
  1. Which of the following is true about the conversion from a CFG to a PDA? a) It is always possible to convert any CFG to an equivalent PDA. b) It is not possible to convert any CFG to an equivalent PDA. c) The resulting PDA will have fewer states than the original CFG. d) The resulting PDA will have more states than the original CFG. Answer: a What is the purpose of converting a CFG to a PDA? a) To reduce the number of rules in the grammar. b) To make it easier to parse input strings. c) To recognize the same language as the CFG. d) To improve the efficiency of the parsing algorithm. Answer: c Which of the following is true about the stack used by the PDA? a) It can only contain terminal symbols. b) It can only contain nonterminal symbols. c) It can contain both terminal and nonterminal symbols. d) It does not play a role in the conversion process. Answer: c Which type of PDA is used for the conversion from a CFG? a) Deterministic PDA (DPDA) b) Non-deterministic PDA (NPDA) c) Both DPDA and NPDA can be used d) None of the above Answer: b Which of the following is true about the acceptance condition of the PDA? a) The PDA must reach the final state to accept the input. b) The PDA must reach the final state and the stack must be empty to accept the input. c) The PDA must reach the final state and the stack must contain at least one symbol to accept the input. d) The PDA must reach the final state and the stack must contain only terminal symbols to accept the input. Answer: b Which of the following is NOT a step in the conversion process? a) Create a start state and a final state for the PDA. b) Create a transition for each rule in the CFG. c) Assign each nonterminal symbol to a unique state in the PDA. d) Remove all nonterminal symbols from the grammar. Answer: d What is the purpose of the transition function in the PDA? a) To move to a new state based on the current input symbol and the top symbol on the stack. b) To generate new symbols to add to the stack. c) To remove symbols from the stack. d) To determine whether the input string is valid or not. Answer: a Which of the following is true about the number of transitions in the PDA? a) The number of transitions is always equal to the number of rules in the grammar. b) The number of transitions can be greater or less than the number of rules in the grammar. c) The number of transitions is always less than the number of rules in the grammar. d) The number of transitions is not related to the number of rules in the grammar. Answer: b Which of the following is true about the conversion from a CFG to a PDA? a) It can only be done for regular languages. b) It can only be done for context-free languages. c) It can be done for any formal language. d) It cannot be done for any formal language. Answer: b Which of the following is true about the role of the stack in the PDA? a) It is used to keep track of the input symbols. b) It is used to keep track of the state of the PDA. c) It is used to keep track of the nonterminal symbols in the input string. d) It is not used in the conversion process


Subjective Short Notes
Midterm & Finalterm Prepration
Past papers included

Download PDF

  1. What is the difference between a CFG and a PDA? Answer: A CFG is a formal grammar that generates a set of strings, while a PDA is a type of automaton that accepts or rejects input strings based on a set of rules. What is the purpose of converting a CFG to a PDA? Answer: The purpose is to create an equivalent PDA that recognizes the same language as the original CFG. What is the stack used for in the PDA? Answer: The stack is used to keep track of symbols as the PDA processes an input string. What is a non-deterministic PDA (NPDA)? Answer: An NPDA is a type of PDA that allows for multiple transitions from a given state, which can lead to multiple possible paths through the automaton. What is the acceptance condition for a PDA? Answer: The acceptance condition is that the PDA must reach a final state and have an empty stack. What is the role of the transition function in the PDA? Answer: The transition function determines how the PDA transitions between states based on the current input symbol and the symbol at the top of the stack. How is each nonterminal symbol in the CFG assigned to a state in the PDA? Answer: Each nonterminal symbol is assigned to a unique state in the PDA. How is each rule in the CFG converted to a transition in the PDA? Answer: Each rule in the CFG is converted to a transition that pushes or pops symbols onto the stack and transitions between states. What is the relationship between the number of transitions in the PDA and the number of rules in the CFG? Answer: The number of transitions in the PDA can be greater or less than the number of rules in the CFG. Can any CFG be converted to an equivalent PDA? Answer: Yes, it is always possible to convert any CFG to an equivalent PDA.

In computer science, a Pushdown Automaton (PDA) is a type of automaton that extends the capabilities of a finite state machine by adding a stack, which allows it to recognize context-free languages. Context-free grammars (CFGs) are a formal way to describe a language, but they cannot be directly processed by a computer. By converting a CFG to a PDA, we can create an equivalent automaton that can be used to recognize the same language. The process of converting a CFG to a PDA involves several steps. First, we create a PDA with a single state that has an empty stack. This state is known as the start state. Next, we assign each nonterminal symbol in the CFG to a unique state in the PDA. We also add a final state to the PDA, which is used to indicate that the input string has been accepted. For each rule in the CFG, we create a transition in the PDA that pops the top symbol from the stack and pushes the right-hand side of the rule onto the stack. The transition also moves the automaton to the appropriate state based on the current input symbol and the symbol at the top of the stack. This process is repeated for every rule in the CFG. Once the PDA has been constructed, it can be used to process input strings. As the input string is read, the PDA transitions between states and manipulates the stack based on the current symbol and the symbol at the top of the stack. If the PDA reaches the final state with an empty stack, the input string is accepted. Otherwise, the input string is rejected. In conclusion, converting a CFG to a PDA is an important technique in formal language theory. It allows us to create an equivalent automaton that can be used to recognize the same language. By understanding the process of conversion, we can gain a deeper understanding of context-free grammars and the languages they generate.

Course Lectures