Question: = = 2. (40 points) For a language L over alphabet I, we define LH-1 = {x2 5* | By * with (2= y= 12|

= = 2. (40 points) For a language L over alphabet

= = 2. (40 points) For a language L over alphabet I, we define LH-1 = {x2 5* | By * with (2= \y= 12| such that ryz E L}. For example, if L = {a, to, cat, math, solve, theory}, then 1 - 1 = {ct, thry}. Prove that if L is regular, then L1 - need not be regular. Hint: Consider the language 0*21* and recall closure properties of regular languages =

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