MHB Are the regular expressions the same?

AI Thread Summary
The discussion centers on whether the intersection of two regular expressions, represented as {a,b,c}* · aba · {a,b,c}* ∩ {a,b,c}* · cbc · {a,b,c}*, is equivalent to a single regular expression combining both patterns. It is clarified that the intersection operation (∩) does not yield a regular expression, as regular expressions are closed under union and concatenation, but not intersection. The expressions in question are not regular due to the presence of the intersection operator. The conclusion emphasizes that while the two forms may represent similar patterns, they are not equivalent as regular expressions. Understanding these properties is crucial for proper manipulation of regular languages.
evinda
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Hi!I have also an other question.

Is the regular expression $\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*}\}\cap\{\{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}\}$ equal to this one: $\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}$ or is there a difference?
 
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$\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*}\}\cap\{\{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}\}$ is not a regular expression because it contains $\cap$.
 
Evgeny.Makarov said:
$\{\{a,b,c\}^{*} \cdot aba \cdot \{a,b,c\}^{*}\}\cap\{\{a,b,c\}^{*} \cdot cbc \cdot \{a,b,c\}^{*}\}$ is not a regular expression because it contains $\cap$.

I understand...Thank you very much! :o
 

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