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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.
Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
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Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
Prove xy+yz+ýz=xy+z
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Give DFA''s accepting the following languages over the alphabet {0,1}: i. The set of all strings beginning with a 1 that, when interpreted as a binary integer, is a multiple of 5.
examples of decidable problems
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