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To prove that 2n1 o(2n), we need to show that the growth rate of 2n1 is strictly less than the growth rate of 2n as n approaches infinity. This can be demonstrated by using the formal definition of little-o notation and showing that the limit of (2n1) / 2n as n approaches infinity is equal to 0.
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What is the total number of all binary strings that do not contain the substring "010"?
The total number of all binary strings that do not contain the substring "010" is 2n1, where n is the length of the binary string.
Is it possible to prove that the clique problem is NP-complete?
Yes, it is possible to prove that the clique problem is NP-complete.
Is it possible to prove that a software component and even an entire program is correct?
No. You can only state correctness to a degree of certainty. That degree might be very high, particularly for a very short routine, but no one can prove correctness to 100%.
Which of these is not a good tip to follow when making Internet purchases?
Use your credit card to prove your identity.
How can you use the pumping lemma to prove that a language is not regular?
To use the pumping lemma to prove that a language is not regular, you would assume the language is regular and then show that there is a string in the language that cannot be "pumped" according to the lemma's conditions. This contradiction would indicate that the language is not regular.
