The Descriptive Complexity of Bayesian Network Specifications

Author(s)

Cozman, Fabio G. ; Maua, Denis D. ; Antonucci, A ; Cholvy, L ; Papini, O

• Document type: Journal article
• Source: SYMBOLIC AND QUANTITATIVE APPROACHES TO REASONING WITH UNCERTAINTY, ECSQARU 2017; v. 10369, p. 11-pg., 2017-01-01.

Abstract

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 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 PPNP, a result that does not seem to have equivalent in the literature. (AU)

• FAPESP's process: 15/21880-4 - PROVERBS -- PRobabilistic OVERconstrained Boolean Systems: reasoning tools and applications
• Grantee: Marcelo Finger
• Support Opportunities: Regular Research Grants