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Generalized Register Context-Free Grammars

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Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

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Abstract

Register context-free grammars (RCFG) is an extension of context-free grammars to handle data values in a restricted way. This paper first introduces register type as a finite representation of the register contents and shows some properties of RCFG. Next, generalized RCFG (GRCFG) is defined by permitting an arbitrary relation on data values in the guard expression of a production rule. We extend register type to GRCFG and introduce two properties of GRCFG, the simulation property and the type oracle. We then show that \(\varepsilon \)-rule removal is possible and the emptiness and membership problems are EXPTIME solvable for GRCFG that satisfy these two properties.

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Notes

  1. 1.

    We exclude the diagonal elements \(\{(i,i)\mid i\in [k]\}\) from the domain of a register type because the applicability of a rule does not depend on whether \(\theta (i)\bowtie \theta (i)\).

  2. 2.

    For readability, we denote a register type as a Boolean formula on a register assignment \(\theta \). For example, \(\gamma _2(1,2)=\mathtt{tt}\) and \(\gamma _2(2,1)=\mathtt{ff}\) if we follow the notation defined in Sect. 4.2.

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Authors and Affiliations

  1. Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa, Nagoya, 464-8601, Japan

    Ryoma Senda & Hiroyuki Seki

  2. Graduate School of Engineering, Kochi University of Technology, Tosayamada, Kami City, Kochi, 782-8502, Japan

    Yoshiaki Takata

Authors
  1. Ryoma Senda
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  2. Yoshiaki Takata
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  3. Hiroyuki Seki
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Correspondence to Ryoma Senda .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Senda, R., Takata, Y., Seki, H. (2019). Generalized Register Context-Free Grammars. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_19

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_19

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  • Online ISBN: 978-3-030-13435-8

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