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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.
As we are primarily concerned with questions of what is and what is not computable relative to some particular model of computation, we will usually base our explorations of langua
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Normal forms are important because they give us a 'standard' way of rewriting and allow us to compare two apparently different grammars G1 and G2. The two grammars can be shown to
The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie
program in C++ of Arden''s Theorem
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De?nition (Instantaneous Description) (for both DFAs and NFAs) An instantaneous description of A = (Q,Σ, δ, q 0 , F) , either a DFA or an NFA, is a pair h q ,w i ∈ Q×Σ*, where
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