Languages Fall 2004 COMP 335 1 A language

Languages Fall 2004 COMP 335 1

A language is a set of strings String: A sequence of letters/symbols Examples: “cat”, “dog”, “house”, … Defined over an alphabet: Fall 2004 COMP 335 2

Alphabets and Strings We will use small alphabets: Strings Fall 2004 COMP 335 3

String Operations Concatenation Fall 2004 COMP 335 4

Reverse Fall 2004 COMP 335 5

String Length: Examples: Fall 2004 COMP 335 6

Length of Concatenation Example: Fall 2004 COMP 335 7

The Empty String A string with no letters: Observations: Fall 2004 COMP 335 8

Substring of string: a subsequence of consecutive characters String Fall 2004 Substring COMP 335 9

Prefix and Suffix Prefixes Suffixes prefix suffix Fall 2004 COMP 335 10

Another Operation Example: Definition: Fall 2004 COMP 335 11

The * Operation : the set of all possible strings from alphabet Fall 2004 COMP 335 12

The + Operation : the set of all possible strings from alphabet except Fall 2004 COMP 335 13

Languages A language is any subset of Example: Languages: Fall 2004 COMP 335 14

Note that: Sets Set size String length Fall 2004 COMP 335 15

Another Example An infinite language Fall 2004 COMP 335 16

Operations on Languages The usual set operations Complement: Fall 2004 COMP 335 17

Reverse Definition: Examples: Fall 2004 COMP 335 18

Concatenation Definition: Example: Fall 2004 COMP 335 19

Another Operation Definition: Special case: Fall 2004 COMP 335 20

More Examples Fall 2004 COMP 335 21

Star-Closure (Kleene *) Definition: Example: Fall 2004 COMP 335 22

Positive Closure Definition: Fall 2004 COMP 335 23