A full-adder is a combinational circuit that forms the arithmetic sum of three input bits.

The pumping lemma says that for any string s in the language, with length greater than the pumping length p, we can write s = xyz with |xy| ≤ p, such that xyi z is also in the language for every i ≥ 0. For the given language, we can take p = 2.

Here are the cases:

Consider any string a i b j c k in the language. If i = 1 or i > 2, we take $x = \epsilon$ and y = a. If i = 1, we must have j = k and adding any number of a’s still preserves the membership in the language. For i > 2, all strings obtained by pumping y as defined above, have two or more a’s and hence are always in the language.

For i = 2, we can take and y = aa. Since the strings obtained by pumping in this case always have an even number of a’s, they are all in the language.
Finally, for the case i = 0, we take $x = \epsilon$ , and y = b if j > 0 and y = c otherwise. Since strings of the form b j c k are always in the language, we satisfy the conditions of the pumping lemma in this case as well.

8 0

2 years ago

What flight patterns do groups of birds utilize and why?

lara31 [8.8K]

Birds mostly fly in a V because the lead bird cuts al of the wind and has the hardest work and then after a while the lead bird goes to the back and another bird takes his place cutting all the wind for the other birds

7 0

2 years ago

An engineer measures a sample of 1200 shafts out of a certain shipment. He finds the shafts have an average diameter of 2.45 inc

Vadim26 [7]

Answer: 78.89%

Explanation:

Given : Sample size : n= 1200

Sample mean : $\overline{x}=2.45$