Bellman's GAP

Abstract

Dynamic programming is a well-established technique to solve combinatorial optimization problems. In several areas of applied computer science, such as operations research, natural language processing, or biosequence analysis, dynamic programming problems arise in many variations and with a considerable degree of sophistication. The simple way dynamic programming problems are normally presented in computer science textbooks -- as a set of table recurrences -- scales poorly for real world problems, where the search space is deeply structured and the scoring model is elaborate. Coming up with pages of correct recurrences is difficult, implementation is error-prone, and debugging is tedious. Algebraic Dynamic Programming (ADP) is a language-independent, declarative approach which alleviates these problems for a relevant class of dynamic programming problems over sequence data.Bellman's GAP implements ADP by providing a declarative language (GAP-L) with a Java-reminiscent syntax, and a compiler (GAP-C) translating declarative programs into C++ code, which is competitive to handwritten code, and arguably more reliable. This article introduces the GAP-L language, demonstrates the benefits of developing dynamic programming algorithms in a declarative framework by educational example, and reports on the practice of programming bioinformatics applications with Bellman's GAP.