Computational Completeness of Simple Semi-conditional Insertion-Deletion Systems
Insertion-deletion (or ins-del for short) systems are well studied in formal language theory, especially regarding their computational completeness. The need for many variants on ins-del systems was raised by the computational completeness result of ins-del system with (optimal) size (1, 1, 1; 1, 1, 1). Several regulations like graph-control, matrix and semi-conditional have been imposed on ins-del systems. Typically, computational completeness are obtained as trade-off results, reducing the size, say, to (1, 1, 0, 1, 1, 0) at the expense of increasing other measures of descriptional complexity. In this paper, we study simple semi-conditional ins-del systems, where an ins-del rule can be applied only in the presence or absence of substrings of the derivation string. We show that simple semi-conditional ins-del system, with maximum permitting string length 2 and maximum forbidden string length 1 and sizes (2, 0, 0; 2, 0, 0), (1, 1, 0; 2, 0, 0), or (1, 1, 0; 1, 1, 1), are computationally complete. We also describe RE by a simple semi-conditional ins-del system of size (1, 1, 0; 1, 1, 0) and with maximum permitting and forbidden string lengths 3 and 1, respectively. The obtained results complement the existing results available in the literature.
- 1.Fernau, H., Kuppusamy, L., Raman, I.: Graph-controlled insertion-deletion systems generating language classes beyond linearity. In: Pighizzini, G., Câmpeanu, C. (eds.) DCFS 2017. LNCS, vol. 10316, pp. 128–139. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60252-3_10CrossRefzbMATHGoogle Scholar
- 3.Fernau, H., Kuppusamy, L., Raman, I.: On describing the regular closure of the linear languages with graph-controlled insertion-deletion systems. In: RAIRO Informatique théorique et Applications/Theoretical Informatics and Applications (2017, Submitted)Google Scholar
- 4.Fernau, H., Kuppusamy, L., Raman, I.: On path-controlled insertion-deletion systems. Accepted with Acta Informatica (2017)Google Scholar
- 10.Kuppusamy, L., Rama, R.: On the power of tissue P systems with insertion and deletion rules. In: Pre-Proceedings of Workshop on Membrane Computing, vol. 28. Report RGML, pp. 304–318. University of Tarragona, Spain (2003)Google Scholar