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Constraint Satisfaction, Graph Isomorphism, and the Pebbling Comonad

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Samson Abramsky on Logic and Structure in Computer Science and Beyond

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 25))

Abstract

The pebbling comonad introduced in (Abramsky, Dawar, Wang 2017) gives a categorical account relating natural approximations of homomorphism and isomorphism. On the one hand we have the local consistency algorithms that approximate homomorphism and on the other the Weisfeiler–Leman algorithms that approximate isomorphism. Both of these have elegant characterizations as pebble games. In this paper we give a brief tour through the background that led to the definition of the pebbling comonad and look at some prospects it offers.

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Notes

  1. 1.

    Here, \(\wp (X)\) denotes the powerset of X.

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Authors and Affiliations

  1. University of Cambridge, Cambridge, England

    Anuj Dawar

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  1. Anuj Dawar
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Correspondence to Anuj Dawar .

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Editors and Affiliations

  1. Department of Ethics, Governance and Society, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Alessandra Palmigiano

  2. Department of Computer Science, University College London, London, UK

    Mehrnoosh Sadrzadeh

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Dawar, A. (2023). Constraint Satisfaction, Graph Isomorphism, and the Pebbling Comonad. In: Palmigiano, A., Sadrzadeh, M. (eds) Samson Abramsky on Logic and Structure in Computer Science and Beyond. Outstanding Contributions to Logic, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-24117-8_18

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