fall 2006costas busch - rpi1 languages. fall 2006costas busch - rpi2 language: a set of strings...
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- Slide 1
- Fall 2006Costas Busch - RPI1 Languages
- Slide 2
- Fall 2006Costas Busch - RPI2 Language: a set of strings String: a sequence of symbols from some alphabet Example: Strings: cat, dog, house Language: {cat, dog, house} Alphabet:
- Slide 3
- Fall 2006Costas Busch - RPI3 Languages are used to describe computation problems: Alphabet:
- Slide 4
- Fall 2006Costas Busch - RPI4 Alphabets and Strings Example Strings Example Alphabet: An alphabet is a set of symbols A string is a sequence of symbols from the alphabet
- Slide 5
- Fall 2006Costas Busch - RPI5 Decimal numbers alphabet Binary numbers alphabet
- Slide 6
- Fall 2006Costas Busch - RPI6 Unary numbers alphabet Unary number: Decimal number:
- Slide 7
- Fall 2006Costas Busch - RPI7 String Operations Concatenation
- Slide 8
- Fall 2006Costas Busch - RPI8 Reverse
- Slide 9
- Fall 2006Costas Busch - RPI9 String Length Length: Examples:
- Slide 10
- Fall 2006Costas Busch - RPI10 Length of Concatenation Example:
- Slide 11
- Fall 2006Costas Busch - RPI11 Empty String A string with no letters is denoted: Observations:
- Slide 12
- Fall 2006Costas Busch - RPI12 Substring Substring of string: a subsequence of consecutive characters String Substring
- Slide 13
- Fall 2006Costas Busch - RPI13 Prefix and Suffix Prefixes Suffixes prefix suffix
- Slide 14
- Fall 2006Costas Busch - RPI14 Another Operation Example: Definition:
- Slide 15
- Fall 2006Costas Busch - RPI15 The * Operation : the set of all possible strings from alphabet
- Slide 16
- Fall 2006Costas Busch - RPI16 The + Operation : the set of all possible strings from alphabet except
- Slide 17
- Fall 2006Costas Busch - RPI17 Languages A language over alphabet is any subset of Examples: Language:
- Slide 18
- Fall 2006Costas Busch - RPI18 More Language Examples An infinite language Alphabet
- Slide 19
- Fall 2006Costas Busch - RPI19 Prime numbers Alphabet Language:
- Slide 20
- Fall 2006Costas Busch - RPI20 Even and odd numbers Alphabet
- Slide 21
- Fall 2006Costas Busch - RPI21 Unary Addition Alphabet: Language:
- Slide 22
- Fall 2006Costas Busch - RPI22 Squares Alphabet: Language:
- Slide 23
- Fall 2006Costas Busch - RPI23 Note that: Sets Set size String length
- Slide 24
- Fall 2006Costas Busch - RPI24 Operations on Languages The usual set operations Complement:
- Slide 25
- Fall 2006Costas Busch - RPI25 Reverse Definition: Examples:
- Slide 26
- Fall 2006Costas Busch - RPI26 Concatenation Definition: Example:
- Slide 27
- Fall 2006Costas Busch - RPI27 Another Operation Definition: Special case:
- Slide 28
- Fall 2006Costas Busch - RPI28
- Slide 29
- Fall 2006Costas Busch - RPI29 Star-Closure (Kleene *) All strings that can be constructed from Definition: Example:
- Slide 30
- Fall 2006Costas Busch - RPI30 Positive Closure Definition: Same with but without the