propertiesbase4

Propertiesbase4 is a term used in theoretical computer science and number theory to describe a class of properties that are defined or verifiable via the base-4 (quaternary) representation of numbers or strings. In this framework, a property is designated as a base-4 property if there exists a mechanism—typically a finite automaton, a regular language, or a first-order logic formula—that can determine whether an object satisfies the property by inspecting its base-4 digits. The focus on base-4 digits means the property is invariant under base-4 encoding and independent of decimal or other representations.

Common examples include forbidding certain substrings of digits, constraining the sum of digits modulo a fixed integer, or enforcing periodic patterns in the quaternary expansion; more generally, the class includes properties definable in the logical theory that uses the ordering of digits, the least significant digit, and digit-wise relations.

The concept is connected to the broader study of automatic structures and numeration systems, where similar properties are studied for other bases such as base-2 and base-10. It has applications in the analysis of digit-driven algorithms, pattern avoidance problems, and the characterization of regular sequences. While not tied to a single formal standard, propertiesbase4 serves as a useful shorthand for discussing how digit-based constraints interact with the quaternary representation in both theoretical and practical contexts.