Declaration of Variables
Name variables
Are variables associated with one another?
Can we mitigate the number of variables?
Are variables associated with one another?
Can we mitigate the number of variables?
Grammars
Structure of grammar L is a language over an alphabet A then a grammar for L α → β α = strings of symbols taken from language A β = strings of symbols from a grammar disjoint from A. Can be interpreted as: replace α by β α produces β α rewrites β α reduces β --- Start symbol S → β Ex. Let A = { a, b, c }. S → Λ | aS | bS | cS Ex. Set of binary numerals that represent odd numbers O → B 1 B → Λ | B 0 | B 1. --- S → AB A → Λ | aA B → Λ | bB. Leftmost derivation S ⇒ AB ⇒ aAB ⇒ aaAB ⇒ aaB ⇒ aabB ⇒ aab . Rightmost Derivation S ⇒ AB ⇒ AbB ⇒ Ab ⇒ aAb ⇒ aaAb ⇒ aab . --- The Language of a Grammar (3.3.4) If G is a grammar with the start symbol S and the set of terminals T , then the language of G is the set L ( G ) = { s | s ∈ T * and S ⇒ + s }. Three simple grammars 1. {Λ, a, aa , …, a n , … } = { a n | n ∈ N}. • S → Λ | aS . 2. {Λ, ab, aabb , …, a n b n , … } = { a n b n
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