twoand

Twoand is a term used in theoretical discussions of logic and reactive programming to denote a dual-input conjunction operator with a temporal synchronization constraint. In this sense, twoand extends the ordinary boolean AND by requiring that both inputs not only be true, but also be observed within a defined time window. The operator is described here as a conceptual tool for illustrating how conjunction can be conditioned on arrival timing in streaming settings.

Formal definition: Let a and b be boolean streams with associated timestamps. A twoand operation with window W yields an output event when there exists a pair of input events (a_i, b_j) such that a_i is true, b_j is true, and |t_i − t_j| ≤ W. The result can be modeled as a boolean signal that is true only for such synchronized pairs; in other cases, the output may be false or omitted depending on the implementation. Variants may use different delay strategies or produce multi-valued outputs to reflect synchronization status.

Applications and implementations: Twoand is used in discussions of sensor fusion, event correlation, and real-time monitoring where both conditions must be affirmed in close temporal proximity. In software, it can be implemented as an operator in streaming libraries, similar to zip, combineLatest, or temporal and gate operators, but with a windowed temporal constraint.

Relation to other concepts and limitations: It is closely related to temporal logic, the standard AND operation, and to windowed combinators in reactive programming. It introduces complexity in semantics and may reduce throughput due to waiting for synchronization. As a hypothetical construct, twoand is not an established standard.