1. Strings and Languages L2Lang

2. Alphabet • (Finite) set of atomic elements / letters • String over • Finite sequence of elements / letters from • Basis: • Inductive step: • Closure: … L2Lang

3. Language over is a subset of . • Examples L2Lang

4. String Concatenation • Signature: string string string • Recursive Definition (cf. defn. of +) concatenation primitive operation L2Lang

5. 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? L2Lang

6. 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. L2Lang