# Peer-reviewed publications

Georg
Sauthoff, Stefan Janssen, and Robert Giegerich.
Bellman’s GAP - a declarative language for dynamic programming.
In *Proceedings of 13th International ACM SIGPLAN Symposium on
Principles and Practice of Declarative Programming*, PPDP '11.
ACM, 2011. [ bib |
.pdf ]

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.

Robert Giegerich
and Georg Sauthoff.
Yield grammar analysis in the Bellman's GAP compiler. In
*Proceedings of the Eleventh Workshop on Language Descriptions,
Tools and Applications*, LDTA '11. ACM, 2011. [ bib |
.pdf ]

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.

# Theses

Georg Sauthoff.
*Bellman's GAP: A 2nd Generation Language and System for
Algebraic Dynamic Programming*. PhD thesis, Bielefeld
University, 2011. [ bib |
.pdf ]

The dissertation describes the new Bellman’s GAP which is a programming system for writing dynamic programming algorithms over sequential data. It is the second generation implementation of the algebraic dynamic programming frame- work (ADP) [Giegerich et al., A discipline of dynamic programming over sequence data. 2004]. The system includes the multi-paradigm language (GAP-L), its compiler (GAP-C), functional modules (GAP-M) and a web site (GAP Pages) to experiment with GAP-L programs. GAP-L includes declarative constructs, e.g. tree grammars to model the search space, and imperative constructs for programming advanced scoring functions. The syntax of GAP-L is similar to C/Java to lower usage barriers. GAP-C translates the high-level and index-free GAP-L programs into efficient C++-Code, which is competitive with handwritten code. It includes a novel table design optimization algorithm, support for dynamic programming (DP) over multiple sequences (multi-track DP), sampling, optional top-down evaluation, various backtracing schemes etc. GAP-M includes modules for use in GAP-L pro- grams. Examples are efficient representations of classification data types and sampling as well as filter helper functions. GAP Pages contain web dialogs for selected text book dynamic programming algorithms implemented in GAP-L. The web dialogs allow interactive ad-hoc experiments with different inputs and combinations of algebras.

Several benchmarks and examples in the dissertation show the practical efficiency of Bellman’s GAP in terms of program runtime and development time.

Georg Sauthoff.
*Java-Backend für den ADP-Compiler*. Diploma thesis, Bielefeld
University, 2007.