An Algebraic Dynamic Programming Approach to the Analysis of Recombinant DNA Sequences

Dynamic programming (DP, for short) is a fundamental programming technique, applicable to great advantage whenever the input to a problem spawns an exponential search space in a structurally recursive fashion, and solutions to subproblems adhere to an optimality principle. No wonder that DP is the predominant paradigm in computational (molecular) biology. Sequence data—DNA, RNA, and proteins—are determined on an industrial scale today. The desire to give a meaning to these molecular data gives rise to an ever increasing number of sequence analysis tasks. Given the mass of these data and the length of these sequences (3 · 10 bases for a bacterial genome, 3 · 10 for the human genome), program efficiency is crucial. DP is used for assembling DNA sequence data from the fragments that are delivered by the automated sequencing machines [1], and to determine the intron/exon structure of genes [3]. It is used to infer function of proteins by homology to other proteins with known function [10, 11], and to determine the secondary structure of functional RNA genes or regulatory elements [15]. In some areas, DP problems arise in such variety that a specific code generation system for implementing the typical DP recurrences has been developed [2]. This system, however, does not support the development or validation of these recurrences.