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Languages

Languages. Language: a set of strings String: a sequence of symbols from some alphabet Example: Strings: cat, dog, house Language: {cat, dog, house}. Alphabet:. Languages are used to describe computation problems:. Alphabet:. Alphabets and Strings.

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Languages

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  1. Languages Costas Busch - RPI

  2. Language: a set of strings • String:a sequence of symbols • from some alphabet • Example: • Strings: cat, dog, house • Language: {cat, dog, house} Alphabet: Costas Busch - RPI

  3. Languages are used to describe computation problems: Alphabet: Costas Busch - RPI

  4. Alphabets and Strings An alphabet is a set of symbols Example Alphabet: A string is a sequence of symbols from the alphabet Example Strings Costas Busch - RPI

  5. Decimal numbers alphabet Binary numbers alphabet Costas Busch - RPI

  6. Unary numbers alphabet Unary number: Decimal number: Costas Busch - RPI

  7. String Operations Concatenation Costas Busch - RPI

  8. Reverse Costas Busch - RPI

  9. String Length • Length: • Examples: Costas Busch - RPI

  10. Length of Concatenation • Example: Costas Busch - RPI

  11. Empty String • A string with no letters is denoted: • Observations: Costas Busch - RPI

  12. Substring • Substring of string: • a subsequence of consecutive characters • String Substring Costas Busch - RPI

  13. Prefix and Suffix • Prefixes Suffixes prefix suffix Costas Busch - RPI

  14. Another Operation • Example: • Definition: Costas Busch - RPI

  15. The * Operation • : the set of all possible strings from • alphabet Costas Busch - RPI

  16. The + Operation : the set of all possible strings from alphabet except Costas Busch - RPI

  17. Languages • A language over alphabet • is any subset of • Examples: Language: Language: Language: Costas Busch - RPI

  18. More Language Examples • An infinite language Alphabet Costas Busch - RPI

  19. Prime numbers Alphabet Language: Costas Busch - RPI

  20. Even and odd numbers Alphabet Costas Busch - RPI

  21. Unary Addition Alphabet: Language: Costas Busch - RPI

  22. Squares Alphabet: Language: Costas Busch - RPI

  23. Note that: Sets Set size Set size String length Costas Busch - RPI

  24. Operations on Languages • The usual set operations • Complement: Costas Busch - RPI

  25. Reverse • Definition: • Examples: Costas Busch - RPI

  26. Concatenation • Definition: • Example: Costas Busch - RPI

  27. Another Operation • Definition: • Special case: Costas Busch - RPI

  28. Costas Busch - RPI

  29. Star-Closure (Kleene *) • All strings that can be constructed from • Definition: • Example: Costas Busch - RPI

  30. Positive Closure • Definition: Same with but without the Costas Busch - RPI

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