Chapter 8: Q24P (page 360)

For each $n$ , exhibit two regular expressions, $R and S$ , of length $poly (n)$ , where $L (R) \neq L (S)$ , but where the first string on which they differ is exponentially long. In other words, $L (R) and L (S)$ must be different yet agree on all strings of length up to $2^{nd}$ for some constant $ε > 0$ .

Short Answer

Expert verified

Every string of the length up to $2^{εn}$ for the constant $ε > 0$ , has been agreed for two regular expression $S and R$ , where $L (R) and L (S)$ must be different.

Step by step solution

To Regular the expression

The two regular expression $S and R$ of the length $poly (n)$ has been exhibited for the $n$ where $L (R) \neq L (S)$ in which they differ in exponentially long.

To Explain the polynomial length and constructed the expression

The polynomial length has been constructed in a way to recognize the $1^{k}$ for each $k$ and expression which are available of every first $n$ prime.

Every $n - 6$ , the $n^{th}$ prime is smaller than $n (lnn + lnlnn)$ . As a result, the first $n$ primes are added in $O (n^{2} logn)$ steps.

Because the first number that isn't a multiple of either of the first prime numbers has an order of $O (n^{2} logn)$ , it can't grow exponentially with $n$ .

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Short Answer

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To Regular the expression

To Explain the polynomial length and constructed the expression

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For each n, exhibit two regular expressions,R and S , of length poly(n), whereL(R)≠L(S), but where the first string on which they differ is exponentially long. In other words,L(R) and L(S) must be different yet agree on all strings of length up to2nd for some constant ε>0.

Short Answer

Step by step solution

To Regular the expression

To Explain the polynomial length and constructed the expression

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Computer Science Textbooks

Computer Programming

Big Data

Algorithms in Computer Science

Data Representation in Computer Science

Game Design in Computer Science

Functional Programming

Study anywhere. Anytime. Across all devices.