For each of these languages, give both a context-free grammar and a push down automaton. Briefly explain how your CFG and PDA work. Your CFG should be relatively simple and contain at most 6 variables. For this question, your PDA cannot be directly convertedfrom your CFG (a)L1={ x#y | x is a prefix of yR, and y∈{a,b}* } ,Σ ={a,b,#} Recall that wR is w written backwards, and u is a prefix of v if v=ut for some stringt.For example  bb#abb  is  in  L1, but  a#ab  is not. (b)L2={ aibjck | i ≥ j or j ≥ k } (c)L3 = {w∈{a,b}* | w contains an unequal number of a’s and b’s}

Database System Concepts
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ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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For each of these languages, give both a context-free grammar and a push down automaton. Briefly explain how your CFG and PDA work. Your CFG should be relatively simple and contain at most 6 variables. For this question, your PDA cannot be directly convertedfrom your CFG

(a)L1={ x#y | x is a prefix of yR, and y{a,b}* } ,Σ ={a,b,#}

Recall that wR is w written backwards, and u is a prefix of v if v=ut for some stringt.For example  bb#abb  is  in  L1, but  a#ab  is not.

(b)L2={ aibjck | i ≥ j or j ≥ k }

(c)L3 = {w{a,b}* | w contains an unequal number of a’s and b’s}

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