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International Colloquium on Theoretical Aspects of Computing

ICTAC 2015: Theoretical Aspects of Computing - ICTAC 2015 pp 404–421Cite as

Undecidability Results for Multi-Lane Spatial Logic

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9399))

Abstract

We consider (un)decidability of Multi-Lane Spatial Logic (MLSL), a multi-dimensional modal logic introduced for reasoning about traffic manoeuvres. MLSL with length measurement has been shown to be undecidable. However, the proof relies on exact values. This raises the question whether the logic remains undecidable when we consider robust satisfiability, i.e. when values are known only approximately. Our main result is that robust satisfiability of MLSL is undecidable. Furthermore, we prove that even MLSL without length measurement is undecidable. In both cases we reduce the intersection emptiness of two context-free languages to the respective satisfiability problem.

Work of the author is supported by the Deutsche Forschungsgemeinschaft (DFG) within the Research Training Group DFG GRK 1765 SCARE.

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Acknowledgements

I thank Manuel Gieseking, Martin Hilscher, Sven Linker, Ernst-Rüdiger Olderog and Maike Schwammberger for helpful discussions and proofreading. Additionally, I would like to thank the anonymous reviewers of this paper and of a previous version of this paper for valuable feedback.

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Authors and Affiliations

  1. Department of Computing Science, University of Oldenburg, Oldenburg, Germany

    Heinrich Ody

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  1. Heinrich Ody
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Correspondence to Heinrich Ody .

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Editors and Affiliations

  1. University of Lübeck, Lübeck, Schleswig-Holstein, Germany

    Martin Leucker

  2. Pontificia Universidad Javeriana-Cali, Cali, Colombia

    Camilo Rueda

  3. Pontificia Universidad Javeriana-Cali, CNRS LIX École Polytechnique de Paris, Palaiseau Cedex, France

    Frank D. Valencia

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Ody, H. (2015). Undecidability Results for Multi-Lane Spatial Logic. In: Leucker, M., Rueda, C., Valencia, F. (eds) Theoretical Aspects of Computing - ICTAC 2015. ICTAC 2015. Lecture Notes in Computer Science(), vol 9399. Springer, Cham. https://doi.org/10.1007/978-3-319-25150-9_24

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  • DOI: https://doi.org/10.1007/978-3-319-25150-9_24

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25149-3

  • Online ISBN: 978-3-319-25150-9

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