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State Grammars with Stores

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Descriptional Complexity of Formal Systems (DCFS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10952))

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Abstract

State grammars are context-free grammars where the productions have states associated with them, and can only be applied to a nonterminal if the current state matches the state in the production. Once states are added to grammars, it is natural to add various stores, similar to machine models. With such extensions, productions can only be applied if both the state and the value read from each store matches between the current sentential form and the production. Here, generative capacity results are presented for different derivation modes, with and without additional stores. In particular, with the standard derivation relation, it is shown that adding reversal-bounded counters does not increase the capacity, and states are enough. Also, state grammars with reversal-bounded counters that operate using leftmost derivations are shown to coincide with languages accepted by one-way machines with a pushdown and reversal-bounded counters, and these are surprisingly shown to be strictly weaker than state grammars with the standard derivation relation (and no counters). Complexity results of some decision problems involving state grammars with counters are also studied.

The research of O. H. Ibarra was supported, in part, by NSF Grant CCF-1117708. The research of I. McQuillan was supported, in part, by Natural Sciences and Engineering Research Council of Canada Grant 2016-06172.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of California, Santa Barbara, CA, 93106, USA

    Oscar H. Ibarra

  2. Department of Computer Science, University of Saskatchewan, Saskatoon, SK, S7N 5A9, Canada

    Ian McQuillan

Authors
  1. Oscar H. Ibarra
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  2. Ian McQuillan
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Corresponding author

Correspondence to Ian McQuillan .

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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, Canada

    Stavros Konstantinidis

  2. Dipartimento di Informatica e Comunicazi, Universita degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

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Ibarra, O.H., McQuillan, I. (2018). State Grammars with Stores. In: Konstantinidis, S., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2018. Lecture Notes in Computer Science(), vol 10952. Springer, Cham. https://doi.org/10.1007/978-3-319-94631-3_14

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  • DOI: https://doi.org/10.1007/978-3-319-94631-3_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94630-6

  • Online ISBN: 978-3-319-94631-3

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