MadeEasy Subject Test: Theory of Computation - Regular Languages

Question

a)every regular languahe on alphabet{0} has the form C^mx+b where m and b are positive integer constants and 0<=X<=infinite

b) A language on alphabet {0} defined by L={0^n ,n is a multiple of 3 } is regular

c) the language {0^m 1^n ; n= 100-m } is regular.

which is false

answr is c

??? i think c also regular

Comments

C is regular just need simplyfication i.e.

n = 100 -m

n + m = 100

Which means that the lenth of the string is at most 100 not more than that which is finite and regular.

Answer 1

I think n+m =100 is given, which is finite but we have to count whether n+m is 100 or not.

As there are several combinations of n,m values like

0,100

1,99

2,98

3,97 .......(100,0)

so we can represent all these combinations in a single DFA

Therefore regular.