Computability and Complexity

Abstract

Once we have the building blocks for a computing device, we can construct the device and give it tasks to perform. Some tasks are more difficult than others. Some tasks may even be impossible for the computing device to perform. This is the concept of computability. Since tasks can be represented as functions, we need to determine the computability of functions. The computable functions are obviously limited by the computing device, but if we choose a sufficiently general computing device it can serve as a measure for computability.