1. 1 Languages

2. 2 A language is a set of strings String: A sequence of letters Examples: “cat”, “dog”, “house”, … Defined over an alphabet:

3. 3 Alphabets and Strings We will use small alphabets: Strings

4. 4 String Operations Concatenation

5. 5 Reverse

6. 6 String Length Length: Examples:

7. 7 Length of Concatenation Example:

8. 8 Empty String A string with no letters: Observations:

9. 9 Substring Substring of string: a subsequence of consecutive characters String Substring

10. 10 Prefix and Suffix Prefixes Suffixes prefix suffix

11. 11 Another Operation Example: Definition:

12. 12 The * Operation : the set of all possible strings from alphabet

13. 13 The + Operation : the set of all possible strings from alphabet except

14. 14 Languages A language is any subset of Example: Languages:

15. 15 Note that: Sets Set size String length

16. 16 Another Example An infinite language

17. 17 Operations on Languages The usual set operations Complement:

18. 18 Reverse Definition: Examples:

19. 19 Concatenation Definition: Example:

20. 20 Another Operation Definition: Special case:

21. 21 More Examples

22. 22 Star-Closure (Kleene *) Definition: Example:

23. 23 Positive Closure Definition:

24. 24 Exercise {a,ba}*