Descriptional complexity of multi-continuous grammars

The present paper discusses multi-continuous grammars and their descriptional complexity with respect to the number of nonterminals. It proves that six-nonterminal multi-continuous grammars characterize the family of recursively enumerable languages. In addition, this paper formulates an open problem area closely related to this characterization

Regulated pushdown automata

The present paper suggests a new investigation area of the formal language theory — regulated automata. Specifically, it investigates pushdown automata that regulate the use of their rules by control languages. It proves that this regulation has no effect on the power of pushdown automata if the control languages are regular. However, the pushdown automata regulated by linear control languages characterize the family of recursively enumerable languages. All these results are established in terms of (A) acceptance by final state, (B) acceptance by empty pushdown, and (C) acceptance by final state and empty pushdown. In its conclusion, this paper formulates several open problems

Final Sentential Forms

Let G be a context-free grammar with a total alphabet V, and let F be a final language over an alphabet W such that W is a subset of V. A final sentential form is any sentential form of G that, after omitting symbols from V - W, it belongs to F. The string resulting from the elimination of all nonterminals from W in a final sentential form is in the language of G finalized by F if and only if it contains only terminals. The language of any context-free grammar finalized by a regular language is context-free. On the other hand, it is demonstrated that L is a recursively enumerable language if and only if there exists a propagating context-free grammar G such that L equals the language of G finalized by {w#w^R | w is a string over a binary alphabet}, where w^R is the reversal of w.Comment: In Proceedings NCMA 2023, arXiv:2309.0733

Two-way metalinear PC grammar systems and their descriptional complexity

Besides a derivation step and a communication step, a two-way PC grammar system can make a reduction step during which it reduces the right-hand side of a context-free production to its left-hand side. This paper proves that every non-unary recursively enumerable language is defined by a centralized two-way grammar system, ┌, with two metalinear components in a very economical way. Indeed, ┌'s master has only three nonterminals and one communication production; furthermore, it produces all sentential forms with no more than two occurrences of nonterminals. In addition, during every computation, ┌ makes a single communication step. Some variants of two-way PC grammar systems are discussed in the conclusion of this paper