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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.
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
The fact that regular languages are closed under Boolean operations simpli?es the process of establishing regularity of languages; in essence we can augment the regular operations
The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗? It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little le
The fundamental idea of strictly local languages is that they are speci?ed solely in terms of the blocks of consecutive symbols that occur in a word. We'll start by considering lan
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Applying the pumping lemma is not fundamentally di?erent than applying (general) su?x substitution closure or the non-counting property. The pumping lemma is a little more complica
These assumptions hold for addition, for instance. Every instance of addition has a unique solution. Each instance is a pair of numbers and the possible solutions include any third
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