Dynamic programming schemata

Abstract

In this paper we give a model of dynamic programming based on functional equations. A general method for solving these equations, based on the fixpoint theory for lattices, is given. Furthermore it is shown that a dynamic programming problem can be formulated in a suitable regular algebra and the system can be solved using Gaussian elimination. A dynamic programming problem can be posed independently of the particular values of functions and constants. Therefore, we introduce three types of dynamic programming schemata. Equivalence of schemata is defined and investigated, and necessary and sufficient conditions are given for the case of positively monotone interpretations.