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Questions about properties of the class of regular languages and individual languages.
3
votes
4
answers
2k
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Language where every prefix has almost equal a's and b's
Is the following language regular?
$$L = \{x \in \{a, b\}^* \mid \text{in every prefix \(w\) of \(x\), } 0 \le |w|_a − |w|_b \le 2\}$$
If so, give a DFA for it with as few states as possible. If you …
-1
votes
1
answer
149
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L is a regular language and w is any word, not necessarily in L. Show that L is regular
$L$ is a regular language and $w$ is any word, not necessarily in $L$. We define the set as
$$L/w = \{x \in \Sigma ^* \mid xw \in L\}.$$
Show that $L/w$ is regular.
I'm really struggling with this …
0
votes
1
answer
2k
views
Showing Context Free Grammars that are regular if and only if L(G) = Σ∗.
Suppose that G is a context-free grammar. How can I show that “Is L(G) regular?” is undecidable. Also, prove that L is always context-free but is regular if and only if L(G) = Σ∗.
This is what I hav …