The Descriptive Complexity of Bayesian Network Specifications

  • Fabio G. CozmanEmail author
  • Denis D. Mauá
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10369)


We adapt the theory of descriptive complexity to Bayesian networks, by investigating how expressive can be specifications based on predicates and quantifiers. We show that Bayesian network specifications that employ first-order quantification capture the complexity class \(\mathsf {PP}\); that is, any phenomenon that can be simulated with a polynomial time probabilistic Turing machine can be also modeled by such a network. We also show that, by allowing quantification over predicates, the resulting Bayesian network specifications capture the complexity class \(\mathsf {PP}^\mathsf {NP}\), a result that does not seem to have equivalent in the literature.



The first author is partially supported by CNPq, grant 308433/2014-9. This paper was partially funded by FAPESP grant #2015/21880-4 (project Proverbs).


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Escola PolitécnicaUniversidade de São PauloSão PauloBrazil
  2. 2.Instituto de Matemática e EstatísticaUniversidade de São PauloSão PauloBrazil

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