Strings and Languages

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Strings and Languages
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• Alphabet
• (Finite) set of atomic elements
• String over
• Finite sequence of elements from
• Basis
• Inductive step
• Closure

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• Language over is a subset of .
• Examples

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String Concatenation

• Signature string string string
• Recursive Definition (cf. defn. of )

concatenation
primitive operation
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• String concatenation is associative.
• Implication
• Order of performing concatenation is immaterial.
• Parenthesis is redundant.
• Other Examples
• and on integers and matrices is
  associative, while - on integers is not.
• Is NAND and NOR on booleans associative?

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• Refer to the text for the proof of associativity
  of the concatenation operation.
• Refer to the text for the definition of reverse
  of a string and its properties.