Identify the class of the language
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1. $L = \{wxw | w,x ∈ \{{a,b}\}^*\} $

Here, <math>L</math> can generate all strings in <math>\Sigma^*</math>, by making <math>x = (a+b)^*</math> and <math>w = \epsilon</math>. Hence, <math>L</math> is regular.


2. $L = \{wxw| w,x ∈ \{{a,b}\}^+\}$

Here, L is not generating all strings in <math>\Sigma^*</math> as the strings like abab are not generated by L. Here, L accepts all strings except those of the form ww, w \in (a+b)^*. To do this is not possible with a PDA and we need a LBA making L CSL.

1.WW | such that W=(a+b)* 2.WW | such that W=(a+b)+ 6.WWr | such that W=(a+b)* 7.WWr| such that W=(a+b)+ 8.1.WXWr | such that W,X=(a+b)* 9.WXWr | such that W,X=(a+b)+

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1. $L = \{wxw | w,x ∈ \{{a,b}\}^*\} $

Here, <math>L</math> can generate all strings in <math>\Sigma^*</math>, by making <math>x = (a+b)^*</math> and <math>w = \epsilon</math>. Hence, <math>L</math> is regular.


2. $L = \{wxw| w,x ∈ \{{a,b}\}^+\}$

Here, L is not generating all strings in <math>\Sigma^*</math> as the strings like abab are not generated by L. Here, L accepts all strings except those of the form ww, w \in (a+b)^*. To do this is not possible with a PDA and we need a LBA making L CSL.

1.WW | such that W=(a+b)* 2.WW | such that W=(a+b)+ 6.WWr | such that W=(a+b)* 7.WWr| such that W=(a+b)+ 8.1.WXWr | such that W,X=(a+b)* 9.WXWr | such that W,X=(a+b)+