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Random Context and Semi-conditional Insertion-deletion Systems

Ivanov S., Verlan S.

Fundamenta Informaticae

2015

Vol. 138, nr 1/2

127--144

In this article we introduce the operations of insertion and deletion working in random context and semi-conditional modes. We show that conditional application of insertion and deletion rules strictly increases the computational power. In the case of semi-conditional insertion-deletion systems, context-free insertion and deletion rules of one symbol are sufficient to achieve computational completeness. In the random context case, our results expose asymmetry between the computational power of insertion and deletion rules: semi-conditional systems of size (2, 0, 0; 1, 1, 0) (with context-free two-symbol insertion rules, and one-symbol deletion rules with one-symbol left context) 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.

Left Random Context ET0L Grammars

Meduna A., Zemek P.

Fundamenta Informaticae

2013

Vol. 123, nr 3

289--304

Consider ET0L grammars. Modify them such that a set of permitting symbols and a set of forbidding symbols are attached to each of their rules, just like in random context grammars. A rule like this can rewrite a symbol if each of its permitting symbols occurs to the left of the symbol to be rewritten in the current sentential form while each of its forbidding symbols does not occur there. ET0L grammars modified in this way are referred to as left random context ET0L grammars, and they represent the principal subject of the investigation in this paper. We prove that these grammars characterize the family of recursively enumerable languages, and without erasing rules, they characterize the family of context-sensitive languages. We also introduce a variety of special cases of these grammars and establish their generative power. In the conclusion, we put all the achieved results into the context of formal language theory as a whole and formulate several open questions.