Dynamic Programming as Graph Searching: An Algebraic Approach

Abstract

Finding the solution of a dynamic programming problem m the form of polyadic functional equatmns is shown to be equivalent to searching a mmmaal cost path in an AND/OR graph with monotone cost functions The proof is given in an algebraic framework and is based on a commutaUvity result between solutton and mterpretauon of a symbohc system This approach Is simdar to the one used by some authors to prove the eqmvalence between the operaUonal and denotatmnal semantics of programming languages. © 1981, ACM. All rights reserved.