Motivation: Dynamic programming is ubiquitous in bioinformatics. Developing and implementing non-trivial dynamic programming algorithms is often error prone and tedious. Bellman’s GAP is a new programming system, designed to ease the development of bioinformatics tools based on the dynamic programming technique.Results: In Bellman’s GAP, dynamic programming algorithms are described in a declarative style by tree grammars, evaluation algebras and products formed thereof. This bypasses the design of explicit dynamic programming recurrences and yields programs that are free of subscript errors, modular and easy to modify. The declarative modules are compiled into C++ code that is competitive to carefully hand-crafted implementations.This article introduces the Bellman’s GAP system and its language, GAP-L. It then demonstrates the ease of development and the degree of re-use by creating variants of two common bioinformatics algorithms. Finally, it evaluates Bellman’s GAP as an implementation platform of ‘real-world’ bioinformatics tools.Availability: Bellman’s GAP is available under GPL license from http://bibiserv.cebitec.uni-bielefeld.de/bellmansgap. This Web site includes a repository of re-usable modules for RNA folding based on thermodynamics.Contact: robert@techfak.uni-bielefeld.deSupplementary information: Supplementary data are available at Bioinformatics online

Dynamic programming algorithms are traditionally expressed by a set of table recurrences -a low level of abstraction which renders the design of novel dynamic programming algorithms difficult and makes debugging cumbersome.Bellman's GAP is a declarative language supporting dynamic programming over sequence data. It implements algebraic dynamic programming and allows specifying algorithms by combining so-called yield grammars with evaluation algebras. Products on algebras allow to create novel types of analysis from already given ones, without modifying tested components. Bellman's GAP extends the previous concepts of algebraic dynamic programming in several respects, such as an "interleaved" product operation and the analysis of multi-track input.Extensive analysis of the yield grammar is required for generating efficient imperative code from the algebraic specification. This article gives an overview of the analyses required and presents three of them in detail. Measurements with "real-world" applications demonstrate the quality of the code produced.

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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.