Regular languages and their generating functions: The inverse problem. The technique of determining a generating function for an unambiguous context-free language is known as the Sch”utzenberger methodology. For regular languages, Elena Barcucci et al. proposed an approach for inverting this methodology based on Soittola’s theorem. This idea allows a combinatorial interpretation (by means of a regular language) of certain positive integer sequences that are defined by C-finite recurrences. In this paper we present a Maple implementation of this inverse methodology and describe various applications. We give a short introduction to the underlying theory, i.e., the question of deciding $mathbb N$-rationality. In addition, some aspects and problems concerning the implementation are discussed; some examples from combinatorics illustrate its applicability.
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References in zbMATH (referenced in 5 articles , 1 standard article )
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- Koutschan, Christoph: Regular languages and their generating functions: The inverse problem (2008)
- Lavallée, Sylvain: $\Bbb Z$-rationality of a certain class of formal series (2008)