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The Golden Chain

The Golden Chain. ε NFA  NFA  DFA REGEX. Regular Expressions . Computations in a semi-ring. Given a weighted graph, find the shortest path connecting any two vertices Given a graph, find its transitive closure Given a finite automaton, find the REGEX describing its language.

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The Golden Chain

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  1. The Golden Chain εNFA  NFA  DFA REGEX

  2. Regular Expressions

  3. Computations in a semi-ring • Given a weighted graph, find the shortest path connecting any two vertices • Given a graph, find its transitive closure • Given a finite automaton, find the REGEX describing its language

  4. DFA and REGEX are equivalent!

  5. From DFA ro Regex: Example Will need:

  6. alternative technique: State Elimination

  7. Algebraic laws

  8. Algebraic laws for REGEX

  9. Properties of Regular Languages

  10. The intuition behind the pumping lemma

  11. example

  12. confuting the regularity of a language

  13. The pumping lemma • Cannot prove that a language is regular • It MIGHT be able to confute that a language is regular • It does not state that in any regular language every sufficiently long string z contains a repeated term, i.e., z =xyyw

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