sameindicating

Sameindicating is a term used to describe the property of two indicators or signals that always convey the same information about a system’s state. In practice, sameindicating denotes that two outputs, sensors, or signals agree in their indication for every possible input or condition.

Formally, consider a finite set S of system states, and two indicator functions a: S -> {0,1} and b: S -> {0,1}. The pair (a, b) is said to be sameindicating if a(s) = b(s) for every s in S. The relation is reflexive, symmetric, and transitive: any indicator is sameindicating with itself, if a is sameindicating with b, then b is with a, and if a and b are sameindicating and b and c are, then a and c are as well. Thus, sameindicating defines an equivalence relation on the family of indicators.

Examples are common in engineering and data analysis. In digital circuits, two display outputs may be sameindicating if they always reflect the same truth value for all input combinations. In reliability engineering, two redundant sensors may be sameindicating if they never disagree under tested conditions, contributing to fault detection and system robustness.

Applications include verification and validation, where sameindicating helps prove consistency between subsystems, and redundancy management, where identifying sameindicating indicators supports simplifying designs without losing information. It also aids testing strategies by highlighting where multiple indicators do not provide new information.

See also: equivalence relation, redundancy, signal integrity, consistency checking.