Random Context and Semi-conditional Insertion-deletion Systems

Abstract

In this article we introduce the operations of insertion and deletion working in a random-context and semi-conditional manner. We show that the conditional use of rules strictly increase the computational power. In the case of semi-conditional insertion-deletion systems context-free insertion and deletion rules of one symbol are sufficient to get the computational completeness. In the random context case our results expose an asymmetry between the computational power of insertion and deletion rules: systems of size (2, 0, 0; 1, 1, 0) are computationally complete, while systems of size (1, 1, 0; 2, 0, 0) (and more generally of size (1, 1, 0; p, 1, 1)) are not. This is particularly interesting because other control mechanisms like graph-control or matrix control used together with insertion-deletion systems do not present such asymmetry.

On the generative capacity of matrix insertion-deletion systems of small sum-norm

“…Several variants of ins-del systems have been considered in the literature, imposing regulation mechanisms on top, motivated by classical formal language theory (Dassow and Pȃun 1989). Some interesting variants (from our perspective) are ins-del P systems (Alhazov et al 2011), tissue P systems with ins-del rules (Kuppusamy and Rama 2003), context-free ins-del systems (Margenstern et al 2005), graph-controlled ins-del systems (Fernau et al 2017b;Freund et al 2010;Ivanov and Verlan 2017), matrix insertion systems (Marcus and Pȃun 1990), matrix ins-del systems (Kuppusamy et al 2011;Petre and Verlan 2012;Kuppusamy and Mahendran 2016), random context and semi-conditional ins-del systems (Ivanov and Verlan 2015), etc. We refer to the survey (Verlan 2010) for more details of several variants of ins-del systems.…”