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On the Complexity of the Conditional Independence Implication Problem with Bounded Cardinalities

Author Michał Makowski

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ACM Subject Classification
  • Mathematics of computing → Information theory
  • Theory of computation → Problems, reductions and completeness
Keywords
  • Conditional independence implication
  • exponential time
  • tiling problem

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Abstract

We show that the conditional independence (CI) implication problem with bounded cardinalities, which asks whether a given CI implication holds for all discrete random variables with given cardinalities, is co-NEXPTIME-hard. The problem remains co-NEXPTIME-hard if all variables are binary. The reduction goes from a variant of the tiling problem and is based on a prior construction used by Cheuk Ting Li to show the undecidability of a related problem where the cardinality of some variables remains unbounded. The CI implication problem with bounded cardinalities is known to be in EXPSPACE, as its negation can be stated as an existential first-order logic formula over the reals of size exponential with regard to the size of the input.

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Michał Makowski. On the Complexity of the Conditional Independence Implication Problem with Bounded Cardinalities. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 73:1-73:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.73

Author Details

Michał Makowski
  • Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland

Acknowledgements

The author would like to thank Damian Niwiński for his guidance and the anonymous reviewers for their valuable comments.

References

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