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A context free grammar G = (N, Σ, P, S) is in binary form if for all productions
A we have |α| ≤ 2. In addition we say that G is in Chomsky Normaml Form (CNF) if it is in binary form and if the only sorts of production have the form
A → a (where a is a terminal symbol)
or
A → BC (where B and C are non-terminals)
We will show that every CFG G is λ- equivalent to a grammar G' that is in CNF (i.e. the only difference between G and G' is that may or may not be included. Since we know how to test for the presence of in our languages we will be able to construct equivalent grammars.
Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
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Explain Theory of Computation ,Overview of DFA,NFA, CFG, PDA, Turing Machine, Regular Language, Context Free Language, Pumping Lemma, Context Sensitive Language, Chomsky Normal For
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We will specify a computation of one of these automata by specifying the pair of the symbols that are in the window and the remainder of the string to the right of the window at ea
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Suppose A = (Q,Σ, T, q 0 , F) is a DFA and that Q = {q 0 , q 1 , . . . , q n-1 } includes n states. Thinking of the automaton in terms of its transition graph, a string x is recogn
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To see this, note that if there are any cycles in the Myhill graph of A then L(A) will be infinite, since any such cycle can be repeated arbitrarily many times. Conversely, if the
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