Reasoning Short Cuts in Infinite Domain Constraint Satisfaction: Algorithms and Lower Bounds for Backdoors

Authors Peter Jonsson, Victor Lagerkvist, Sebastian Ordyniak

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Author Details

Peter Jonsson
  • Department of Computer and Information Science, Linköping University, Sweden
Victor Lagerkvist
  • Department of Computer and Information Science, Linköping University, Sweden
Sebastian Ordyniak
  • Algorithms Group, University of Sheffield, UK


We thank the anonymous reviewers for several useful comments.

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Peter Jonsson, Victor Lagerkvist, and Sebastian Ordyniak. Reasoning Short Cuts in Infinite Domain Constraint Satisfaction: Algorithms and Lower Bounds for Backdoors. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere, and the algorithmic problem of finding such backdoors has consequently been intensively studied. Sioutis and Janhunen (KI, 2019) have proposed a generalised backdoor concept suitable for infinite-domain CSP instances over binary constraints. We generalise their concept into a large class of CSPs that allow for higher-arity constraints. We show that this kind of infinite-domain backdoors have many of the positive computational properties that finite-domain backdoors have: the associated computational problems are fixed-parameter tractable whenever the underlying constraint language is finite. On the other hand, we show that infinite languages make the problems considerably harder.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Discrete mathematics
  • Theory of computation → Complexity theory and logic
  • Constraint Satisfaction Problems
  • Parameterised Complexity
  • Backdoors


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