Strings and Languages cs466(Prasad) L2Lang

Alphabet String over (Finite) set of atomic elements / letters Finite sequence of elements / letters from Basis: Inductive step: Closure: … cs466(Prasad) L2Lang

Language over is a subset of . Examples cs466(Prasad) L2Lang

String Concatenation Recursive Definition (cf. defn. of +) Signature: string string string Recursive Definition (cf. defn. of +) concatenation primitive operation cs466(Prasad) L2Lang

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? cs466(Prasad) L2Lang

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. cs466(Prasad) L2Lang