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Commutative Rational Term Rewriting

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Language and Automata Theory and Applications (LATA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12638))

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Abstract

Term rewriting for rational terms, i.e. infinite terms with a finite number of different subterms, has been considered e.g. in Corradini & Gadducci (1998) and Aoto & Ketema (2012). In this paper, we consider rational term rewriting by a set of commutativity rules i.e. rules of the form \(f(x,y) \rightarrow f(y,x)\), based on the framework of Aoto & Ketema (2012). A rewrite step with a commutativity rule is specified via a regular set of redex positions, thus via a finite automaton. We present some finite automata constructions that correspond to (in particular) taking inverse rewrite steps, merging two branching rewrite steps, and merging two consecutive rewrite steps. As a corollary, we show that rational rewrite steps by the commutativity rules are closed under taking equivalence of the rewrite steps.

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Notes

  1. 1.

    To ease the readability, however, we omit below the equation \(x_\bot = \bot (x_\bot ,\ldots ,x_\bot )\) if the equation is not necessary, i.e. if there is no equation in E such that its right hand side is a variable or all \(f \in \mathcal {F}\) originally have the same arity.

References

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Acknowledgement

Thanks are due to anonymous referees and Akihisa Yamada for helpful comments. This work was partially supported by a grant from JSPS No. 18K11158.

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Authors and Affiliations

  1. Niigata University, Niigata, Japan

    Mamoru Ishizuka & Takahito Aoto

  2. Simane University, Shimane, Japan

    Munehiro Iwami

Authors
  1. Mamoru Ishizuka
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  2. Takahito Aoto
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  3. Munehiro Iwami
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Corresponding author

Correspondence to Takahito Aoto .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Alberto Leporati

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. Ariel University, Ariel, Israel

    Dana Shapira

  4. University of Milano-Bicocca, Milan, Italy

    Claudio Zandron

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Ishizuka, M., Aoto, T., Iwami, M. (2021). Commutative Rational Term Rewriting. In: Leporati, A., Martín-Vide, C., Shapira, D., Zandron, C. (eds) Language and Automata Theory and Applications. LATA 2021. Lecture Notes in Computer Science(), vol 12638. Springer, Cham. https://doi.org/10.1007/978-3-030-68195-1_15

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  • DOI: https://doi.org/10.1007/978-3-030-68195-1_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-68194-4

  • Online ISBN: 978-3-030-68195-1

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