The communicative and associative nature of the way reduction operators process their data enables the subtasks of an operator to be processed independently, and is thus highly connected to concurrency and parallelism. Consequently, various topics in concurrent programming could be related to reduction operators, and by applying the same principles of reduction operators, problems regarding those topics could be made more intuitive and efficient.

As we have seen, add and multiply operators are reduction operators. More generally, number-crunching problems that usually involve communicative and associative operators are prime candidates for applying concurrency and parallelism. This is actually a true case for the famous, and arguably one of the most used modules in Python—NumPy, whose code is implemented to be as parallelizable as possible.

Furthermore, applying the logic operators AND, OR, or XOR to an array of Boolean values works the same way as reduction operators. Some real-world applications for concurrent bitwise reduction operators include the following:

• Finite state machines, which commonly take advantage of logic operators while processing logic gates. Finite state machines can be found in both hardware structures and software designs.
• Communication across sockets/ports, which typically involves parity and stop bits to check for data errors, or flow control algorithms. These techniques utilize logic values of individual bytes to process information through the use of logic operators.
• Compression and encryption techniques, which heavily depend on bitwise algorithms.