Notationsserie

Notationsserie is a term used in theoretical computer science and mathematics to describe a structured sequence of notations, where each element in the series represents a distinct encoding or representation rule for expressing objects. The word combines notation with series, signaling a progression of encodings rather than a single system.

Formal concept. A notationsserie can be modeled as a sequence of encoding functions f_i from a domain D to strings over a finite alphabet A, with i ranging over the natural numbers. In many treatments, later elements in the series extend or refine earlier ones, providing more expressive power or finer detail while preserving compatibility with earlier encodings. The idea emphasizes how objects can be represented in multiple, hierarchically related ways.

Examples. Classical numeral systems form a simple notationsserie: decimal, binary, and other base-k representations encode natural numbers with different alphabets and rules. Prefix notation for arithmetic expressions and postfix (Reverse Polish) notation are additional, distinct encodings of the same syntactic objects. In logic, Gödel numbering offers another notationsserie, encoding syntactic items as natural numbers to facilitate meta-mania reasoning about proofs and formulas.

Applications. Notationsserie concepts help analyze and compare encoding schemes, study unique decodability and efficiency, and support formal verification, compiler design, and data interchange. They also aid in teaching by illustrating how the same object can be represented in multiple, progressively detailed ways.

Related ideas include encoding, numeral systems, formal grammars, and Gödel numbering. While not always standard terminology, notationsserie serves as a concise way to discuss hierarchies of representation and their properties.