On the Size Complexity of Non-Returning Context-Free PC Grammar Systems

TL;DR

This paper demonstrates that any recursively enumerable language can be generated by a non-returning parallel communicating grammar system with only six context-free components, and introduces a universal system for unary languages with fixed size parameters.

Contribution

It improves the known bounds for non-returning PC grammar systems and presents a universal system with fixed size parameters for unary languages.

Findings

Any recursively enumerable language can be generated with six components.

A universal non-returning PC grammar system for unary languages is constructed.

Size parameters of the universal system are independent of the language.

Abstract

Improving the previously known best bound, we show that any recursively enumerable language can be generated with a non-returning parallel communicating (PC) grammar system having six context-free components. We also present a non-returning universal PC grammar system generating unary languages, that is, a system where not only the number of components, but also the number of productions and the number of nonterminals are limited by certain constants, and these size parameters do not depend on the generated language.