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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 be equal provided they have the same normal form.
Additionally by rewriting grammars in a standard way we have a structure that can form the input to future stages of a process. For example programs in a high level programming languages have to be converted in more 'basic' instructions via a parser and it is helpful if the inputs to such a process are of a uniform type.
In this section we introduce one of the standard normal forms commonly used; this is known as Chomsky Normal Form.
One might assume that non-closure under concatenation would imply non closure under both Kleene- and positive closure, since the concatenation of a language with itself is included
Automaton (NFA) (with ε-transitions) is a 5-tuple: (Q,Σ, δ, q 0 , F i where Q, Σ, q 0 and F are as in a DFA and T ⊆ Q × Q × (Σ ∪ {ε}). We must also modify the de?nitions of th
examples of decidable problems
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It is not hard to see that ε-transitions do not add to the accepting power of the model. The underlying idea is that whenever an ID (q, σ v) directly computes another (p, v) via
Proof (sketch): Suppose L 1 and L 2 are recognizable. Then there are DFAs A 1 = (Q,Σ, T 1 , q 0 , F 1 ) and A 2 = (P,Σ, T 2 , p 0 , F 2 ) such that L 1 = L(A 1 ) and L 2 = L(
Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
program in C++ of Arden''s Theorem
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