Introduction to algorithms
Algebra of programming
Proceedings of the 5th International Conference on Intelligent Systems for Molecular Biology
Implementing Algebraic Dynamic Programming in the Functional and the Imperative Programming Paradigm
MPC '02 Proceedings of the 6th International Conference on Mathematics of Program Construction
A discipline of dynamic programming over sequence data
Science of Computer Programming - Methods of software design: Techniques and applications
Table design in dynamic programming
Information and Computation
Compiling Comp Ling: practical weighted dynamic programming and the Dyna language
HLT '05 Proceedings of the conference on Human Language Technology and Empirical Methods in Natural Language Processing
Bellman's GAP: a declarative language for dynamic programming
Proceedings of the 13th international ACM SIGPLAN symposium on Principles and practices of declarative programming
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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.