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Context-Free Grammars – Regular Grammars

Context-Free Grammars – Regular Grammars. Lecture 14 Section 2.1 Fri, Sep 21, 2007. Regular Grammars. Yet another way to describe regular languages is through regular grammars . Start symbol S . Set of variables V . Set of terminal symbols  . Set of rules R. Regular Grammars.

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Context-Free Grammars – Regular Grammars

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  1. Context-Free Grammars – Regular Grammars Lecture 14 Section 2.1 Fri, Sep 21, 2007

  2. Regular Grammars • Yet another way to describe regular languages is through regular grammars. • Start symbolS. • Set of variablesV. • Set of terminal symbols. • Set of rulesR.

  3. Regular Grammars • Each rule is of one of the following forms: • A aB • A  where A and B are variables and a is a terminal.

  4. Regular Grammars • Then we begin with the start symbol and apply rules until we obtain a string of all terminals.

  5. Example • Let the rules be • S aX • S  bY • S   • X  aS • X  bZ • X   • :

  6. Example • Y  aY • Y  bY • Y   • Z  aY • Z  bX

  7. Example • What strings can be obtained by these rules? • One example: • S aX  aaS  aabY  aab. • Another example: • S bY  bbY  bbaY  bba.

  8. The Language of a Grammar • The set of all strings obtainable from the grammar, by starting with the start symbol, is called the language of the grammar.

  9. Regular Grammars and Regular Languages • It is easy to derive a regular grammar from a DFA, and vice versa.

  10. Regular Grammars and Regular Languages • Given a DFA, • Let V be the set of states Q. • The start symbol is the start state. • For each transition (p, a) = q, write a rule p  aq. • For each accept state q, write a rule q  . • This process is reversible.

  11. Example • Construct a DFA from the previous example. • What is the language of the grammar?

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