Abstract
We develop a theory of algebraic operations over linear grammars that makes it possible to combine simple atomic grammars operating on single sequences into complex, multi-dimensional grammars. We demonstrate the utility of this framework by constructing the search spaces of complex alignment problems on multiple input sequences explicitly as algebraic expressions of very simple 1-dimensional grammars. The compiler accompanying our theory makes it easy to experiment with the combination of multiple grammars and different operations. Composite grammars can be written out in ${\hbox{\LaTeX}}$ for documentation and as a guide to implementation of dynamic programming algorithms. An embedding in Haskell as a domain-specific language makes the theory directly accessible to writing and using grammar products without the detour of an external compiler. http://www.bioinf.uni-leipzig.de/Software/gramprod/
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