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 for REGEX
Properties of Regular Languages
The intuition behind the pumping lemma
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