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Two Power-Decreasing Derivation Restrictions in Generalized Scattered Context Grammars
Tomás Masopust, Alexander Meduna, and Jirě Simácek
Abstract (in LaTeX format)
The present paper introduces and discusses generalized scattered context grammars that are based upon sequences of productions whose left-hand sides are formed by nonterminal strings, not just single nonterminals. It places two restrictions on the derivations in these grammars. More specifically, let $k$ be a positive integer. The first restriction requires that all rewritten symbols occur within the first $k$ symbols of the first continuous block of nonterminals in the sentential form during every derivation step. The other restriction defines derivations over sentential forms containing no more than $k$ occurrences of nonterminals. As its main result, the paper demonstrates that both restrictions decrease the generative power of these grammars to the power of context-free grammars.
Keywords: scattered context grammar, grammatical generalization, derivation restriction, generative power.
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BibTeX entry
@ARTICLE{Masopust:2008:ActaCybernetica,author = {Tom\'{a}\v{s} Masopust and Alexander Meduna and Ji\v{r}\'{i} \v{S}im\'{a}\v{c}ek},
title = {Two Power-Decreasing Derivation Restrictions in Generalized Scattered Context Grammars},
journal = {Acta Cybernetica},
year = {2008},
volume = {18},
pages = {783--793},
number = {4},
abstract = {The present paper introduces and discusses generalized scattered context grammars that are based upon sequences of productions whose left-hand sides are formed by nonterminal strings, not just single nonterminals. It places two restrictions on the derivations in these grammars. More specifically, let $k$ be a positive integer. The first restriction requires that all rewritten symbols occur within the first $k$ symbols of the first continuous block of nonterminals in the sentential form during every derivation step. The other restriction defines derivations over sentential forms containing no more than $k$ occurrences of nonterminals. As its main result, the paper demonstrates that both restrictions decrease the generative power of these grammars to the power of context-free grammars.},
keywords = {scattered context grammar, grammatical generalization, derivation restriction, generative power}
}