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International Joint Conference on Automated Reasoning

IJCAR 2018: Automated Reasoning pp 439–454Cite as

Deciding the First-Order Theory of an Algebra of Feature Trees with Updates

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10900))

Abstract

We investigate a logic of an algebra of trees including the update operation, which expresses that a tree is obtained from an input tree by replacing a particular direct subtree of the input tree, while leaving the rest unchanged. This operation improves on the expressivity of existing logics of tree algebras, in our case of feature trees. These allow for an unbounded number of children of a node in a tree.

We show that the first-order theory of this algebra is decidable via a weak quantifier elimination procedure which is allowed to swap existential quantifiers for universal quantifiers. This study is motivated by the logical modeling of transformations on UNIX file system trees expressed in a simple programming language.

This work has been partially supported by the ANR project CoLiS, contract number ANR-15-CE25-0001.

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Acknowledgments

The idea of investigating update constraints on feature trees originates from discussions with Gert Smolka a long time ago. We would like to thank the anonymous reviewers for their useful remarks and suggestions, and the members of the CoLiS project for numerous discussions on tree constraints and their use in modeling tree operations, in particular Claude Marché, Kim Nguyen, Joachim Niehren, Yann Régis-Gianas, Sylvain Salvati, and Mihaela Sighireanu.

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Authors and Affiliations

  1. Univ. Paris Diderot, Sorbonne Paris Cité, IRIF, UMR 8243 CNRS, Paris, France

    Nicolas Jeannerod & Ralf Treinen

Authors
  1. Nicolas Jeannerod
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  2. Ralf Treinen
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Correspondence to Nicolas Jeannerod .

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Editors and Affiliations

  1. Université de Lorraine, Vandoeuvre-lès-Nancy, France

    Didier Galmiche

  2. Baden-Wuerttemberg Cooperative State University, Stuttgart, Germany

    Stephan Schulz

  3. University of Trento, Trento, Italy

    Roberto Sebastiani

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Jeannerod, N., Treinen, R. (2018). Deciding the First-Order Theory of an Algebra of Feature Trees with Updates. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds) Automated Reasoning. IJCAR 2018. Lecture Notes in Computer Science(), vol 10900. Springer, Cham. https://doi.org/10.1007/978-3-319-94205-6_29

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  • DOI: https://doi.org/10.1007/978-3-319-94205-6_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94204-9

  • Online ISBN: 978-3-319-94205-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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