1. Fall 2004COMP 3351 Languages

2. Fall 2004COMP 3352 A language is a set of strings String: A sequence of letters/symbols Examples: “cat”, “dog”, “house”, … Defined over an alphabet:

3. Fall 2004COMP 3353 Alphabets and Strings We will use small alphabets: Strings

4. Fall 2004COMP 3354 String Operations Concatenation

5. Fall 2004COMP 3355 Reverse

6. Fall 2004COMP 3356 String Length Length: Examples:

7. Fall 2004COMP 3357 Length of Concatenation Example:

8. Fall 2004COMP 3358 The Empty String A string with no letters: Observations:

9. Fall 2004COMP 3359 Substring Substring of string: a subsequence of consecutive characters String Substring

10. Fall 2004COMP 33510 Prefix and Suffix Prefixes Suffixes prefix suffix

11. Fall 2004COMP 33511 Another Operation Example: Definition:

12. Fall 2004COMP 33512 The * Operation : the set of all possible strings from alphabet

13. Fall 2004COMP 33513 The + Operation : the set of all possible strings from alphabet except

14. Fall 2004COMP 33514 Languages A language is any subset of Example: Languages:

15. Fall 2004COMP 33515 Note that: Sets Set size String length

16. Fall 2004COMP 33516 Another Example An infinite language

17. Fall 2004COMP 33517 Operations on Languages The usual set operations Complement:

18. Fall 2004COMP 33518 Reverse Definition: Examples:

19. Fall 2004COMP 33519 Concatenation Definition: Example:

20. Fall 2004COMP 33520 Another Operation Definition: Special case:

21. Fall 2004COMP 33521 More Examples

22. Fall 2004COMP 33522 Star-Closure (Kleene *) Definition: Example:

23. Fall 2004COMP 33523 Positive Closure Definition: