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Weighted iterated linear control

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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

  1. We refer to [10, Section 5] for a thorough explanation of \((\Gamma \times C)^+\).

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Acknowledgements

The authors would like to thank the anonymous referees for their careful reading, pointing out mistakes, and suggesting improvements.

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Authors and Affiliations

  1. Institute of Informatics, University of Szeged, Árpád tér 2., Szeged, 6720, Hungary

    Zoltán Fülöp

  2. Faculty of Computer Science, Technische Universität Dresden, 01062, Dresden, Germany

    Heiko Vogler

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  1. Zoltán Fülöp
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  2. Heiko Vogler
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Correspondence to Zoltán Fülöp.

Additional information

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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