XORlike

XORlike is a term used in computer science and logic to describe a family of operations that resemble the exclusive OR (XOR) in their parity-based behavior and algebraic properties. It refers not to a single fixed operator, but to a class of parity-like combining rules that generalize XOR to different input sizes or value domains.

In the classical Boolean setting, an XORlike operation often behaves as parity: the output is 1 if an odd number of inputs are 1, and 0 otherwise. For two inputs this reduces to the standard XOR. When extended to bitstrings or vectors, XORlike operations typically correspond to addition modulo 2 (the arithmetic of GF(2)); such operations are generally associative and commutative, and flipping any single input toggles the output.

Generalizations of XORlike appear in multi-valued logics or in linear-algebraic models over GF(2). In these contexts, parity-based combining rules maintain the idea of “counting mod 2” rather than relying on conventional conjunction or disjunction. The term is often used informally to distinguish parity-based combining from other Boolean operators, while preserving the core notion that the result reflects the parity of truth values.

Applications of XORlike concepts include error detection and correction schemes that use parity checks, digital circuit design with parity bits or linear feedback mechanisms, and certain cryptographic constructions that leverage XOR-like diffusion properties. While XORlike is not a formal operator with a universal definition, it serves as a useful shorthand for parity-based, XOR-inspired operations across various settings.

Related topics include XOR, XNOR, the parity function, and linear operations over GF(2).