Separation of Correctness and Complexity in Algorithm Design

In this paper we propose a new approach to the design of algorithms. This approach is based on the view that all algorithms are composed of a computation and a control component, and that these components can be designed separately. The computation component is responsible for the correctness of an algorithm. It embodies the computational knowledge about a problem domain that is needed to solve the corresponding problem. The control component governs complexity aspects of the solution method by directing the usage of the computational knowledge. This bisection allows the problem of how to construct an algorithm to be split into two smaller problems: "What are the elementary units of computational knowledge for the problem at hand?" and "In what order should these units be used to (efficiently) obtain a solution." This way, the concerns of correctness and complexity are separated. We assert that there are many advantages in separating correctness and complexity in algorithm design. Hence, we examine properties of programming formalisms that influence the possibility of separating the design of the computation and control components of an algorithm.