In this paper we investigate insertion grammars and explore their capacity to generate words parallelly by introducing parallel derivation (where more than one rule can be applied to the string in parallel) and maximum parallel derivation (where as many rules as possible are applied to the string in parallel). We compare the generative power of these grammars with context sensitive and context free grammars and with different variants of contextual grammars. We apply these grammars to syllabification in Romanian and provide arguments that they can also be used in a cognitive perspective.
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Insertion grammars have been introduced in [1] and their computational power has been studied in several places. In [7] it is proved that insertion grammars with weight at least 7 can characterize recursively enumerable languages (modulo a weak coding and an inverse morphism), and the question was formulated whether or not this result can be improved. In this paper, we come up with a positive answer to this question, by decreasing the weight of the insertion grammar used to 5. We also give a characterization of recursively enumerable languages in terms of right quotients of insertion languages.
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Generally, in P systems with string-objects one uses the Chomsky way of rewriting for processing the objects. In this paper we consider the contextual way of handling string-objects in P systems. We introduce some variants of contextual grammars and prove that contextual P systems with rules corresponding to these variants are more powerful than ordinary contextual grammars and their variants. We also show that one-sided contextual P systems with right-sided erased contexts and insertion contextual P systems with right-sided erased contexts are computationally complete.
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