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Two-Way Metalinear PC Grammar Systems and Their Descriptional Complexity
Abstract (in LaTeX format)
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, $\Gamma$, with two metalinear components in a very economical way. Indeed, $\Gamma$'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, $\Gamma$ makes a single communication step. Some variants of two-way PC grammar systems are discussed in the conclusion of this paper.
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BibTeX entry
@article{Meduna:2004:ActaCybernetica,author = {Alexander Meduna},
title = {Two-Way Metalinear PC Grammar Systems and Their Descriptional Complexity},
journal = {Acta Cybernetica},
year = {2004},
volume = {16},
number = {3},
pages = {385--397},
abstract = {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, $\Gamma$, with two metalinear components in a very economical way. Indeed, $\Gamma$'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, $\Gamma$ makes a single communication step. Some variants of two-way PC grammar systems are discussed in the conclusion of this paper.}
}