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0

$begingroup$

If $f$ is a function of integers, define $f(L)$ to be
$$
w mid textfor some $x$, with $.
$$

Show that if $L$ is a regular language, then so if $f(L)$, if $f$ is one of the following functions:

1. 
   $f(n)=n^2$ (i.e., the amount we take has length equal to the square root of what we do not take)


2. $f(n)=2^n$

This is a question from John Hopcroft's Introduction to Automata Theory, that is, Exercise 4.2.9.
And I find it hard to construct a automata like what we do in this question.

automata

share|cite|improve this question

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

$endgroup$

add a comment | 

0

$begingroup$

If $f$ is a function of integers, define $f(L)$ to be
$$
w mid textfor some $x$, with $.
$$

Show that if $L$ is a regular language, then so if $f(L)$, if $f$ is one of the following functions:

1. 
   $f(n)=n^2$ (i.e., the amount we take has length equal to the square root of what we do not take)


2. $f(n)=2^n$

This is a question from John Hopcroft's Introduction to Automata Theory, that is, Exercise 4.2.9.
And I find it hard to construct a automata like what we do in this question.

automata

share|cite|improve this question

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

$endgroup$

add a comment | 

$begingroup$

If $f$ is a function of integers, define $f(L)$ to be
$$
w mid textfor some $x$, with $.
$$

Show that if $L$ is a regular language, then so if $f(L)$, if $f$ is one of the following functions:

1. 
   $f(n)=n^2$ (i.e., the amount we take has length equal to the square root of what we do not take)


2. $f(n)=2^n$

This is a question from John Hopcroft's Introduction to Automata Theory, that is, Exercise 4.2.9.
And I find it hard to construct a automata like what we do in this question.

automata

share|cite|improve this question

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

$endgroup$

share|cite|improve this question

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

share|cite|improve this question

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

edited Mar 24 at 3:00

J.-E. Pin

18.6k21754

asked Mar 22 at 9:52

My_LuluMy_Lulu

125

asked Mar 22 at 9:52

My_LuluMy_Lulu

125