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Which among the following options are correct?Statement 1: TMs can accept languages that are not accepted by any PDA with one stack.Statement 2: But PDA with two stacks can accept any language that a TM can accept.
- a)Statement 1 and 2, both are correct
- b)Statement 1 is correct but Statement 2 is false
- c)Statement 2 is correct while Statement 1 is false
- d)Statement 1 and 2, both are false
Correct answer is option 'A'. Can you explain this answer?
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Which among the following options are correct?Statement 1: TMs can acc...
Both the statements are true. Both the statements are properties of Multistack machines.
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Which among the following options are correct?Statement 1: TMs can acc...
Statement 1: TMs can accept languages that are not accepted by any PDA with one stack.
A Turing Machine (TM) is a theoretical computing machine that can simulate the logic of any computer algorithm. It consists of an input tape, a tape head, a set of states, and a transition function. TMs are more powerful than Pushdown Automata (PDA) because they have an infinite tape and can perform unbounded computation.
A PDA with one stack is a finite automaton with a single stack that can accept languages generated by context-free grammars. It has a limited amount of memory and cannot perform unbounded computation like a TM.
Therefore, Statement 1 is correct. TMs can accept languages that are not accepted by any PDA with one stack because they have more computational power and can perform unbounded computation.
Statement 2: But PDA with two stacks can accept any language that a TM can accept.
A PDA with two stacks is a finite automaton with two stacks that can accept languages generated by context-sensitive grammars. It has more computational power than a PDA with one stack because it can use the additional stack to perform more complex operations.
However, it is not true that a PDA with two stacks can accept any language that a TM can accept. TMs are more powerful than PDAs with two stacks because they have an infinite tape and can perform unbounded computation. TMs can solve problems that are beyond the capabilities of PDAs with two stacks.
Therefore, Statement 2 is false. A PDA with two stacks cannot accept any language that a TM can accept.
Conclusion:
- Statement 1 is correct. TMs can accept languages that are not accepted by any PDA with one stack.
- Statement 2 is false. A PDA with two stacks cannot accept any language that a TM can accept.
Hence, the correct answer is option 'A' - Statement 1 and 2, both are correct.
A Turing Machine (TM) is a theoretical computing machine that can simulate the logic of any computer algorithm. It consists of an input tape, a tape head, a set of states, and a transition function. TMs are more powerful than Pushdown Automata (PDA) because they have an infinite tape and can perform unbounded computation.
A PDA with one stack is a finite automaton with a single stack that can accept languages generated by context-free grammars. It has a limited amount of memory and cannot perform unbounded computation like a TM.
Therefore, Statement 1 is correct. TMs can accept languages that are not accepted by any PDA with one stack because they have more computational power and can perform unbounded computation.
Statement 2: But PDA with two stacks can accept any language that a TM can accept.
A PDA with two stacks is a finite automaton with two stacks that can accept languages generated by context-sensitive grammars. It has more computational power than a PDA with one stack because it can use the additional stack to perform more complex operations.
However, it is not true that a PDA with two stacks can accept any language that a TM can accept. TMs are more powerful than PDAs with two stacks because they have an infinite tape and can perform unbounded computation. TMs can solve problems that are beyond the capabilities of PDAs with two stacks.
Therefore, Statement 2 is false. A PDA with two stacks cannot accept any language that a TM can accept.
Conclusion:
- Statement 1 is correct. TMs can accept languages that are not accepted by any PDA with one stack.
- Statement 2 is false. A PDA with two stacks cannot accept any language that a TM can accept.
Hence, the correct answer is option 'A' - Statement 1 and 2, both are correct.
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Which among the following options are correct?Statement 1: TMs can accept languages that are not accepted by any PDA with one stack.Statement 2: But PDA with two stacks can accept any language that a TM can accept.a)Statement 1 and 2, both are correctb)Statement 1 is correct but Statement 2 is falsec)Statement 2 is correct while Statement 1 is falsed)Statement 1 and 2, both are falseCorrect answer is option 'A'. Can you explain this answer?
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