Which type of gateway is designed to wait for specific named inbound paths to complete?

The correct choice is Complex. A Complex Gateway in BPMN (Business Process Model and Notation) is specifically designed to manage multiple incoming and outgoing paths based on specific conditions. It allows for finer-grained control over process flow compared to other types of gateways.

This type of gateway can wait for certain named inbound paths to complete, making it suitable for scenarios where specific criteria must be met before the process can proceed. For instance, in complex workflows where various tasks may finish at different times, a Complex Gateway can specify that only when certain predefined paths have been completed will the flow continue down the specified outgoing path.

In contrast, other gateways such as AND, OR, and XOR each have distinct functionalities that don't focus on named completion paths. The AND gateway requires that all incoming paths complete before moving forward, the OR gateway allows the flow to progress when any one of its incoming paths completes, and the XOR (exclusive OR) allows only one path to be taken from multiple options based on conditions. None of these options provide the same level of specificity and flexibility in waiting for designated paths as the Complex Gateway does.