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Networks of evolutionary processors: computationally complete normal forms

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Abstract

Networks of evolutionary processors (NEPs, for short) form a bio-inspired language generating computational model that was shown to be equivalent to the model of phrase-structure grammars. In this paper, we analyse different restricted variants of NEPs that preserve the computational power of the general model. We prove that any recursively enumerable language can be generated by a NEP where the derivation rules can be applied at arbitrarily chosen positions, the control of the communication is done by finite automata with at most three states, and either the rule sets are singletons or the underlying graph is a complete graph. If one uses networks with arbitrary underlying graphs and allows the additional application of insertions and deletions only to the right-most or the to left-most position of the derived words for some nodes, then we only need automata with only one state to control the communication in the network. Clearly, this result is optimal; moreover, finite automata with two states are necessary and sufficient in order to generate all the recursively enumerable languages when the derivation rules can be applied only at arbitrarily chosen positions.

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Acknowledgments

Florin Manea’s work was partially supported by the Alexander von Humboldt Foundation through a Research Fellowship at the Otto-von-Guericke University Magdeburg, Germany, between July 2009 and June 2011 and a subsequent Return Fellowship at the University of Bucharest, Romania, between July 2011 and October 2011. His work is currently supported by DFG—Deutsche Forschungsgemeinschaft through the grant 582014.

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Dassow, J., Manea, F. & Truthe, B. Networks of evolutionary processors: computationally complete normal forms. Nat Comput 11, 595–607 (2012). https://doi.org/10.1007/s11047-012-9331-z

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