Chapter 0: Q5E (page 1)

Question: Each of the following languages is the complement of a simpler language. In each part, construct a DFA for the simpler language, and then use it to give the state diagram of a DFA for the language given. In all parts, $Σ = \{a, b\}$ .
$a . \{w | w does not contain the substring ab\} A b . {w | w does not contain the substring baba} c . {w | w contains neither the substrings ab nor ba} d . {w | w is any string not in a * b } e . {w | w is any string not in (ab +) } f . {w | w is any string not in a * \cup b *} g . {w | w is any string that doesnt contain exactly two as} h . {w | w is any string except a and b}$

Short Answer

Expert verified

(a)The complementary of a simplified language $\bar{L} = {w | w L i s i n d e e d t h e l a n g u a g e \bar{L}$ is indeed the language $\bar{L}$ does not include substring ab

(b) L = w it does not contains / allow sub-string as ab .

(d)Go together of L=w does not contains sub-string.

(e)L=w contains neither .

$(f) L = w i n a * b * . (g) L = w n o t i n a * b * . (h) L = w i n (a b +) * . (i) L = w not i n (a b +) * . (j) L = w i n a * + b * . (k) L = w n o t i n a * + b * . (l) L = w i n (a b +) * . (m) L = w h a s e x a c t l y 2 a' s (n) L = w d o e s n o t h a v e e x a c t l y 2 a' s$

Step by step solution

Simple language

In the above question we can see there is total different part of question. Let’s see step by step in short here in step-1. A. Part show that it doesn’t contain any substring. B. Part show that it’s not contain substring like baba which is different than part A.

Part C is not containing any substrings which is either ab or ba . Same way other part is display multiplication and addition related string. And checking weather this string contains or not.

prefix, infix and post fix operation of alphabet

a. L = w contains / accepts sub-string ab . The complementary of a simplified language $\bar{L} = {w | w L i s i n d e e d t h e l a n g u a g e \bar{L}$ does not include substring ab . Then it's only a matter of saying "contain the string ab ." The language L is recognised by DFA as follows: