Abstract
A regulated extension of an insertion-deletion system known as graph-controlled insertion-deletion (GCID) system has several components and each component contains some insertion-deletion rules. A rule is applied to a string in a component and the resultant string is moved to the target component specified in the rule. When resources are so limited (especially, when deletion is context-free) then GCID systems are not known to describe the class of recursively enumerable languages. Hence, it becomes interesting to find the descriptional complexity of such GCID systems of small sizes with respect to language classes below \(\mathrm {RE}\). To this end, we consider closure classes of linear languages. We show that whenever GCID systems describe \(\mathrm {LIN}\) with t components, we can extend this to GCID systems with just one more component to describe, for instance, 2-\(\mathrm {LIN}\) and with further addition of one more component, we can extend to GCID systems that describe the rational closure of \(\mathrm {LIN}\).
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Notes
- 1.
In [12], \(\mathfrak {L}\,\) was called \(\mathcal {L}_*\), which we avoid due to possible confusions with our Kleene closure operator notation.
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Acknowledgments
Some part of the work done by the second author was during the author’s visits to University of Trier, Germany in June-July and December 2016. The possibility to use some overhead money from a DFG grant to support this stay is gratefully acknowledged.
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Fernau, H., Kuppusamy, L., Raman, I. (2017). Graph-Controlled Insertion-Deletion Systems Generating Language Classes Beyond Linearity. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_10
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DOI: https://doi.org/10.1007/978-3-319-60252-3_10
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