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The symbol Z0 in formal definition of PDA is used for

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Consider the NPDA ?Q = {q0, q1, q2}, ? = {0, 1}, ? = {0, 1, ?}, ?, q0, ?, F = {q2}?, where (as per usual convention) Q is the set of states, ? is the input alphabet, ? is stack alphabet, ? is the state transition function, q0 is the initial state, ? is the initial stack symbol, and F is the set of accepting states, The state transition is as following
Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton? 
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2.
Consider the following context-free grammars:

Which one of the following pairs of languages is generated by G1 and G2, respectively

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3.
Which of the following is a simulator for non deterministic automata?
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4.
State true or false:Statement: For every CFL, G, there exists a PDA M such that L(G) = L(M) and vice versa.
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5.
Define for a context free language L ? {0, 1}* ,  init(L)={u ? uv ? L for some v in {0,1}?} ( in other words, init(L) is the set of prefixes of L) Let L = {w ? w is nonempty and has an equal number of 0
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