Abstract
We combine three extensions of context-free grammars: (a) associating its nonterminals with storage configurations, (b) equipping its rules with weights, and (c) controlling its derivations. For a commutative semiring K, we introduce the class of weighted languages generated by K-weighted linear context-free grammars with storage S and with derivations controlled by (S, K)-recognizable weighted languages. The control on the derivations can be iterated in a natural way. We characterize the n-th iteration of the control in terms of the n-th iteration of the one-turn pushdown operator on the storage S of the control weighted language. Moreover, for each proper semiring we prove that iterating the control yields an infinite, strict hierarchy of classes of weighted languages.
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Notes
We refer to [10, Section 5] for a thorough explanation of \((\Gamma \times C)^+\).
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The authors would like to thank the anonymous referees for their careful reading, pointing out mistakes, and suggesting improvements.
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Research of this author was supported by the NKFI Grant no K 108448.
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Fülöp, Z., Vogler, H. Weighted iterated linear control. Acta Informatica 56, 447–469 (2019). https://doi.org/10.1007/s00236-018-0325-x
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DOI: https://doi.org/10.1007/s00236-018-0325-x