Prove that the following language is not regular {anbncn} = {Λ, abc, aabbcc, aaabbbccc, ...}.
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Prove that the following language is not regular {anbncn} = {Λ, abc, aabbcc, aaabbbccc, ...}.
Suppose that L is a regular language. Prove that the language p
r e f i x (L )={w |
x, wx
L } is regular. (For example, if L = {abc, def}, prefix(L) = {?,
a, ab, abc, d, de, def}.)
Prove that for each regular language L the following language is regular: shift(L) = {uv | vu ∈ L}
Just for this problem, let the alphabet be I = { a b c}. Let us consider the language anbncn = { abc aabbcc aaabbbccc ... } Prove that this language is nonregular by the (i) Pumping lemma. Show this by pumping x,y,z
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.
10. Consider the following CFG: Is the language generated by this CFG a regular language? If so, give a regular expression denoting it. If not, prove it.
1/ Assume that A and B are regular language, then prove that i/ (AUB) a regular language ii/ ( A and B) a regular language iii/ A concatenate B a regular language
3. Use the pumping lemma to prove the following language is not regular . Use the pumping lemma to prove the following language is not regular Where is the stringwbut with all the Os replaced by Is and all the し1 = {te E Σ.ead I te _ wu) is replaced by 0s. For example, if w = 00110 then w = 11001.
3. (20 pt.) Prove that the following language is not regular using the closure properties of regular languages. C = {0"1"|m,n0 and mon} Hint: find a regular language L such that CNL is not regular and use the closure properties of regular languages to show that this means that C is not regular.
If L is a regular language, prove that the language {uv : u ∈L, v ∈LR} is also regular
2. If L is a regular language, prove that the language 11 = { uv/ u E 1 , |v|-2) is also regular. (Hint: Can you build an NFA of L1 using an NFA of a language L? Use N, the NFA of the language L)
Prove that the following language is regular or explain why it is nonregular: L = {amb" (m is odd and n is even) OR (m is even and n is odd))