Is L1 L2 a regular language?
(h) If L? = L1 ? L2 is a regular language and L1 is a regular language, then L2 is a regular language. (i) Every regular language has a regular proper subset. (j) If L1 and L2 are nonregular languages, then L1 ? L2 is also not regular. 4. Show that the language L = {anbm : n ? m} is not regular. 5.
How to find the number of consecutive a's modulo n read so far?
Show that for each n >= 1, the language B nis regular. For each n>=1, we built a DFA with the n states q 0 , q 1, …, q n-1to count the number of consecutive a’s modulo n read so far. For each character a that is input, the counter increments by 1 and jumps to the next state in M. It accept the string if and only if the machine stops at q 0.
Is L a regular language?
If L is a regular language, then so is L? = {w : w ? and wR ? L}. If C is any set of regular languages, ?C (the union of all the elements of C) is a regular language. (g) L = {xyxR : x, y ? ?*} is regular. (h) If L? = L1 ? L2 is a regular language and L1 is a regular language, then L2 is a regular language.
How to find if L' is not regular?
7. First, let L' = L ? a*b*, which must be regular if L is. We observe that L' = anbn+2 : n ? 0. Now use the pumping lemma to show that L' is not regular in the same way we used it to show that anbn is not regular. 8. We use the pumping lemma.
Additional Material Section 2.1