Abstract
In this paper, we propose a hierarchy of families of languages generated by networks of evolutionary processors where the filters belong to several special classes of regular sets. More precisely, we show that the use of filters from the class of ordered, non-counting, power-separating, circular, suffix-closed regular, union-free, definite, and combinational languages is as powerful as the use of arbitrary regular languages and yields networks that can generate all the recursively enumerable languages. On the other hand, the use of filters that are only finite languages allows only the generation of regular languages, but not every regular language can be generated. If we use filters that are monoids, nilpotent languages, or commutative regular languages, we obtain one and the same family of languages which contains non-context-free languages but not all regular languages. These results seem to be of interest because they provide both upper and lower bounds on the families of languages that one can use as filters in a network of evolutionary processors in order to obtain a complete computational model.
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Acknowledgments
Florin Manea’s work was partially supported by the Alexander von Humboldt Foundation, through a two-years Research Fellowship at the Otto-von-Guericke University Magdeburg, Germany, that ended in June 2011 and a subsequent Return Fellowship at the University of Bucharest, Romania, between July 2011 and October 2011.
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This paper is an extended version of the contribution presented at the 5th International Conference on Language and Automata Theory and Applications (LATA), Tarragona (Spain), May 2011, LNCS 6838, 262–273.
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Dassow, J., Manea, F. & Truthe, B. Networks of evolutionary processors: the power of subregular filters. Acta Informatica 50, 41–75 (2013). https://doi.org/10.1007/s00236-012-0172-0
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DOI: https://doi.org/10.1007/s00236-012-0172-0