Regular Expressions

1
Regular Expressions
2
Equivalences

• A regular expression describes a set of strings
• For every regular expression, there is a regular
  grammar that generates the same strings
• For every regular grammar there is a
  deterministic finite automata that recognizes the
  strings that the grammar generates.

3
Definition Regular Expression

• Let V be a finite alphabet. A regular expression
  on V is any finite string of symbols from the set
• a a e V U U, , (,), ?, Ø
• That may be formed according to the following
  rules
• ? is a regular expression
• Ø is a regular expression
• If a e V, a is a regular expression
• If a and ß are regular expressions, then so are
• (a ß)
• (a U ß)
• (a)

4
Examples

• Let V 0,1
• Then (10)1 is a regular expression describing
  the set of strings of alternating 1s and 0s that
  start and end with a 1.