When Is L(S ∩ T) Not Equal to L(S) ∩ L(T)?

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SUMMARY

The discussion centers on the relationship between the languages of two sets, S and T, specifically when L(S ∩ T) is not equal to L(S) ∩ L(T). The user initially seeks an example to illustrate this inequality, indicating that elements in L(S) intersect L(T) may not be present in the span of S intersect T. Ultimately, the user resolves their query independently, suggesting that the problem is solvable with a clear understanding of language theory.

PREREQUISITES
  • Understanding of formal languages and automata theory
  • Familiarity with the concepts of language intersection and span
  • Knowledge of the properties of language equivalence
  • Experience with examples of non-equivalent languages
NEXT STEPS
  • Study the properties of language intersection in formal language theory
  • Explore examples of languages where L(S ∩ T) differs from L(S) ∩ L(T)
  • Learn about the implications of language span in automata
  • Investigate the role of context-free and regular languages in intersection properties
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The discussion is beneficial for students and researchers in computer science, particularly those focusing on formal language theory, automata, and computational linguistics.

TrapMuzik
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Okay, so for the problem before this, I proved that L(S ∩ T ) ⊂ L(S ) ∩ L(T ).

For this problem, I have to give an example where L(S ∩ T ) ̸= L(S ) ∩ L(T ).

So I'm thinking that there are going to be elements in L(S) intersect L(T) that are not in the span of S intersect T. In what sort of case would this happen? I'm not sure what direction to go in.

Thanks!
 
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Figured it out! Never mind
 

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