Information Inequality Problem over Set Functions

Author Miika Hannula

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Miika Hannula
  • University of Helsinki, Finland

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Miika Hannula. Information Inequality Problem over Set Functions. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Information inequalities appear in many database applications such as query output size bounds, query containment, and implication between data dependencies. Recently Khamis et al. [Mahmoud Abo Khamis et al., 2020] proposed to study the algorithmic aspects of information inequalities, including the information inequality problem: decide whether a linear inequality over entropies of random variables is valid. While the decidability of this problem is a major open question, applications often involve only inequalities that adhere to specific syntactic forms linked to useful semantic invariance properties. This paper studies the information inequality problem in different syntactic and semantic scenarios that arise from database applications. Focusing on the boundary between tractability and intractability, we show that the information inequality problem is coNP-complete if restricted to normal polymatroids, and in polynomial time if relaxed to monotone functions. We also examine syntactic restrictions related to query output size bounds, and provide an alternative proof, through monotone functions, for the polynomial-time computability of the entropic bound over simple sets of degree constraints.

Subject Classification

ACM Subject Classification
  • Theory of computation → Database theory
  • entropy
  • information theory
  • worst-case output size
  • computational complexity


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