Consider the two languages below:
L1 = {w | w є {0,1,2}* and is of the form 0i1j2k where i, j
and k ≥ 0 and i = j or j = k}
L2 = {w | w є {0,1,2}* and is of the form 0i1j2k where i, j
and k ≥ 0}
One of the languages in the above problem is regular. Which
one? Prove it.
Prove that the OTHER one is not regular.
Is the non-regular one context...
Formal Languages
Give a regular expression for each of the following
languages:
L2a = {w ? {0,1}* | w corresponds to the binary encoding of
non-negative integers that are evenly divisible by 4
L2b = {w ? {a,b}* | w contains at least one 'a' and exactly two
b's}
L2c = {w ? {0, 1, 2}* | w starts with a 2, ends with a 1 and
contains an even number of 0's}.
Are the following languages over {a, b} regular? If they are
then prove it. If they are not prove it with the Pumping Lemma
a) {ap | p is a prime number}
b) {xax | x Î{a,b}*} (start by listing some strings
in, not in, the language
The first five questions give languages over {0, 1}. In each
case decide whether the language is regular or not, and prove your
answer is correct.
5. The set of strings in which the number of 0's is a perfect
square.
Consider the set of vectors S = {(1, 0, 1),(1, 1, 0),(0, 1,
1)}.
(a) Does the set S span R3?
(b) If possible, write the vector (3, 1, 2) as a linear
combination of the vectors in S. If not possible, explain why.
Consider the following statements,
[ 0 , 1 ] × [ 0 , 1 ] with the dictionary order is
complete.
[ 0 , 1 ] × [ 0 , 1 ) with the dictionary order is
complete.
[ 0 , 1 ) × [ 0 , 1 ] with the dictionary order is
complete.
Where the dictionary order on R × R is given by ( a , b
) < ( x , y ) if either a...
Consider the following equation: W =P(1−u)
Suppose that the markup of goods prices over marginal cost is
5%, the real wage is 0.952 and the natural rate of unemployment is
4.8%. What happens to the natural rate of unemployment when the
markup of prices over costs increases to 10%? Graph the result and
explain the logic of your answer.