# 1.3 regular expressions

## Formal Def of a Regular Expression

Say that R is a regular expression if R is: - for some in the alphabet - - - () - () - ()

() are regualr expressions(inductive def)

### some conclusions

- L(R): the language of R
- concatenating the empty set to any set yields the empty set, so

## Equivalence with Finite Automata

- hint: regular language is one that is recognized by some finite automation
- a language is regular iff some regular expression describes it
- prove see textbook p67 p70
**GNFA**: generalized nondeterministic finite automation, its transition arrows may have any regular expression as labels