Abstract
This article investigates insertion–deletion systems of small size, where at most two symbols can be used in the description of insertion or deletion rules in a context-free or contextual manner. The basic result shows a characterization by context-free grammars of insertion–deletion systems, which insert or delete one symbol in one symbol left context (systems of size (1, 1, 0; 1, 1, 0)). If context-free insertion or deletion rules are considered (systems of size (2, 0, 0; 1, 1, 0) or (1, 1, 0; 2, 0, 0)), then we show that corresponding systems are not computationally complete. However, if the insertion and the deletion operations having same size as above are considered in the distributed framework of P systems, then the computational power strictly increases and the obtained models become computationally complete. The article also shows that if context-free insertion and deletion rules of two symbols (of size (2, 0, 0; 2, 0, 0)) are used in combination with P systems, then the obtained model is still not computationally complete. Finally some open problems are presented.
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Acknowledgments
The first author acknowledges the support PIF program of University Rovira i Virgili, and project no. MTM2007-63422 from the Ministry of Science and Education of Spain. The second author acknowledges the support of European Commission, project MolCIP, MIF1-CT-2006-021666. The second and the third author acknowledge the Science and Technology Center in Ukraine, project 4032. The authors would like to acknowledge the anonymous referees for their very helpful comments.
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Krassovitskiy, A., Rogozhin, Y. & Verlan, S. Computational power of insertion–deletion (P) systems with rules of size two. Nat Comput 10, 835–852 (2011). https://doi.org/10.1007/s11047-010-9208-y
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DOI: https://doi.org/10.1007/s11047-010-9208-y