38 Lecture - Nondeterministic PDA

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38 Lecture

CS402

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Nondeterministic PDA

A nondeterministic pushdown automaton (NPDA) is a theoretical model of computation that extends the capabilities of a deterministic pushdown automaton (DPDA) by allowing multiple possible transitions from a given state on the same input symbol.


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  1. What is the primary difference between deterministic pushdown automata (DPDA) and nondeterministic pushdown automata (NPDA)? A. DPDA can have multiple possible transitions on the same input symbol. B. NPDA can have multiple possible transitions on the same input symbol. C. DPDA has a stack and an input tape, while NPDA only has a stack. D. NPDA has a stack and an input tape, while DPDA only has a stack. Solution: B Which of the following is true for an NPDA? A. It always accepts the input string if it has a valid path. B. It always rejects the input string if it has an invalid path. C. It may accept or reject the input string depending on the valid path. D. It always accepts the input string, regardless of the path. Solution: C Which of the following is a valid component of an NPDA? A. Input alphabet B. Stack alphabet C. Transition function D. All of the above Solution: D Can an NPDA have multiple start states? A. Yes B. No Solution: B Which of the following is true for an empty stack in an NPDA? A. It means the machine rejects the input string. B. It means the machine accepts the input string. C. It means the machine halts, but its acceptance or rejection is undefined. D. None of the above. Solution: B Which of the following is true for a language that can be recognized by an NPDA? A. It must be a regular language. B. It must be a context-free language. C. It must be a context-sensitive language. D. It can be any type of language. Solution: B Which of the following is not a valid operation for an NPDA? A. Push a symbol onto the stack B. Pop a symbol from the stack C. Read an input symbol D. Write an input symbol Solution: D Which of the following is true for a nondeterministic choice in an NPDA? A. It always leads to the acceptance of the input string. B. It always leads to the rejection of the input string. C. It may lead to the acceptance or rejection of the input string. D. It does not affect the acceptance or rejection of the input string. Solution: C Which of the following is not a valid way to represent an NPDA? A. A state transition diagram B. A formal definition involving a 5-tuple of components C. A context-free grammar D. A computation tree Solution: C Which of the following is true for the time complexity of an NPDA? A. It is always exponential. B. It is always polynomial. C. It can be either exponential or polynomial. D. It is always constant. Solution: C


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  1. What is a nondeterministic pushdown automaton (NPDA)? Answer: A theoretical model of computation that extends the capabilities of a deterministic pushdown automaton (DPDA) by allowing multiple possible transitions from a given state on the same input symbol. What is the primary difference between a DPDA and an NPDA? Answer: The primary difference is that an NPDA can have multiple possible transitions from a given state on the same input symbol, while a DPDA can only have one. What is a valid component of an NPDA? Answer: A 5-tuple consisting of a set of states, an input alphabet, a stack alphabet, a transition function, and a set of accepting states. Can an NPDA have multiple start states? Answer: No, an NPDA can only have one start state. What does it mean for an NPDA to accept an input string? Answer: It means that there exists at least one valid path through the machine's states and stack that leads to an empty stack at the end of the input. Can an NPDA accept an input string with an invalid path? Answer: No, an NPDA can only accept an input string if there exists at least one valid path through the machine's states and stack. What is a nondeterministic choice in an NPDA? Answer: A nondeterministic choice is when the machine has multiple possible transitions from a given state on the same input symbol, and it chooses one of them nondeterministically. What is a computation tree in an NPDA? Answer: A tree-like representation of the possible paths the machine can take through its states and stack on a given input string. What is the time complexity of an NPDA? Answer: It can be either exponential or polynomial, depending on the specific machine and input. Can an NPDA recognize a language that is not context-free? Answer: No, an NPDA can only recognize context-free languages.

A nondeterministic pushdown automaton (NPDA) is a theoretical model of computation that extends the capabilities of a deterministic pushdown automaton (DPDA) by allowing multiple possible transitions from a given state on the same input symbol. It is a type of automaton that uses a stack to recognize context-free languages. An NPDA consists of a 5-tuple: a set of states, an input alphabet, a stack alphabet, a transition function, and a set of accepting states. The machine starts in an initial state and reads symbols from the input string one at a time. The transition function maps the current state, input symbol, and stack symbol to a set of possible next states and stack symbols. The machine can choose any of the possible next states and stack symbols nondeterministically. An NPDA accepts an input string if there exists at least one valid path through the machine's states and stack that leads to an empty stack at the end of the input. If no valid path exists, the machine rejects the input string. The machine can also enter an infinite loop if there is a cycle in its state transitions. A computation tree is a tree-like representation of the possible paths the machine can take through its states and stack on a given input string. Each node in the tree represents a configuration of the machine, which consists of a state and a stack contents. The tree can be used to determine whether a string is accepted or rejected by the machine. The time complexity of an NPDA can be either exponential or polynomial, depending on the specific machine and input. In general, an NPDA can recognize any language that can be recognized by a context-free grammar. However, it cannot recognize languages that are not context-free. NPDA has various applications in computer science and software engineering. It is used in compilers and parsers to recognize programming languages and translate code. It is also used in natural language processing, pattern recognition, and speech recognition. The concept of NPDA is also essential in the study of computational complexity theory, formal language theory, and automata theory.

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