The Golden Chain

εNFA 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

DFA and REGEX are equivalent!

From DFA ro Regex: Example

Will need:

alternative technique: State Elimination

Algebraic laws

Algebraic laws for REGEX

Properties of Regular Languages

The intuition behind the pumping lemma

example

confuting the regularity of a language

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