We investigate the specification and implementation of iterator components for dyadic Boolean operations in the setting of stream functions and state transition machines.We explicate the approach for the Boolean conjunction and study iterator components repeating this operation. The strict conjunction, the left-strict conjunction, the right-strict conjunction and the parallel conjunction differ in their reaction how they process FALSE-elements from one input channel while waiting for input on the other input channel. We systematically transform the input/output behaviour into state-based implementations using a common history abstraction function.Beyond the particular application, we present general methods for the systematic design of iterator components in distributed systems with asynchronous communication.