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$L_{1}=\left\{a^{n}b^{n}c^{n}|n>=0\right\}\\
L_{2}=\left\{b^{i}c^{j}|i,j>=0\right\}\\
Find \ out\ L_{1}/L_{2}$

2 Answers

2 votes
2 votes
  • L1= {anbncn | >=0}
  • L2 = {b*c*}

L1 / L=  {$\epsilon$ , abc/$\epsilon$ , abc /b , abc/c , aabbcc/ $\epsilon$ , aabbcc/b, aabbcc/bb, aabbcc/c, aabbcc/cc, aabbcc/bbc, aabbcc/bbcc........}​​

 = {$\epsilon$ abc, ab, aabbcc, aabbc, aabb, aab, aa......}

= {a* , anbncn, anbn , anbncn-1, ....}

= {anbncn| >=0 } - {bncn| >=0} -{cn| >=0}$\cup$ $\epsilon$ $\cup${ anbn| >=0 } $\cup$ {an| >=0} $\cup$ many more

edited by
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1 votes

L = L1/L2

L = {x | such that xy belongs to L1 and y belongs to L2}

It means L will consider those strings from the language L1 which have suffix from the language L2, and L removes the suffix part and keep it in the language.

$L1 = {a^nb^nc^n | n>=0}$
$L2 = {b^*c^*}$

L1/L2 = {$a^n b^n c^n$ | n>=0} U {$a^n$ | n>=1} U {$a^n b^n$ | n>=1} U {$a^nb^nc^*$}

Strings in L1/L2 = eps, a, ab, abc, aabbc, aabbcc etc..

edited by

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