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75 lines
1.7 KiB
Markdown
75 lines
1.7 KiB
Markdown
# Symbols, alphabets, and langauges and Regular Grammars
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Alphabet : A set of characters.
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Sigma = { a, b }
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Langauge : A set of strings over a particular alphabet.
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L1(Sigma) = { a, aa, b, ab, ba, bba, .. } (Infinite)
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L2(Sigma) = { aa, bb, ab, ba }; (Length = 2, Finite)
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Any time you constrain a langauge you are
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defining a formal grammar.
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## Formal Grammars:
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FormalGrammer = (Non-Terminals, Terminals, Productions, Starting Symbol)
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Non-Terminals : Variables (can be subsituted with a value)
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Terminals : Cannot be replaced by anything (constant)
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Productions : Rule in the grammar
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**G = (N, T, P, S)**
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Ex:
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```
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S -> aX
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X -> b
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```
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**(This notation is known as BNF : Bakus-Naur Form)**
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Ex.Non-Terminals = S, X
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Ex.Terminals = a, b
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Ex.Productions = S -> aX, X -> b (2)
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Ex.Starting Symbol = S
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Only valid string : "ab"
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## Chomsky Hierachy :
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0. Unrestricted : Natural Langauges, Turing Machines
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1. Context-Sensitive : Programming Languages (Almost all in production)
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2. Context-Free : Programming Langauges (Parsing Syntax only)
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3. Regular : Regular Expressions
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The lower in the hiearchy the less expressive it is.
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RegExp is a vomit inducing terse notation that is equivalent to BNF.
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BNF : RegExp
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S -> aS :
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S -> bA : `a*bc*`
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A -> epsilon :
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A -> cA :
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epsilon : "The empty string".
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Regular expressions may only have one non-terminal:
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* A the very right side (right-linear, RHS)
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* At the very left side (left-linear, LHS)
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Regular expression have no support for *NESTING*
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They can be *RECURSIVE*
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Context-free grammers support nesting.
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Ex:
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(( () ))
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`Parenthesis balacing`
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Non-regular RegExp can support nesting but are not pure
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finite automata and are slower implementation.
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