Hybrid Probabilistic Programs: Algorithms and Complexity

TL;DR

This paper classifies Hybrid Probabilistic Programs into three classes, providing algorithms and complexity analysis for computing consequences, entailment, and consistency, highlighting when polynomial solutions are feasible.

Contribution

It introduces a classification of HPPs and offers algorithms and complexity results for reasoning tasks, clarifying tractability boundaries.

Findings

Algorithms for computing all ground consequences of HPPs.

Complexity results for entailment and consistency problems.

Identification of classes where polynomial algorithms are possible.

Abstract

Hybrid Probabilistic Programs (HPPs) are logic programs that allow the programmer to explicitly encode his knowledge of the dependencies between events being described in the program. In this paper, we classify HPPs into three classes called HPP_1,HPP_2 and HPP_r,r>= 3. For these classes, we provide three types of results for HPPs. First, we develop algorithms to compute the set of all ground consequences of an HPP. Then we provide algorithms and complexity results for the problems of entailment ("Given an HPP P and a query Q as input, is Q a logical consequence of P?") and consistency ("Given an HPP P as input, is P consistent?"). Our results provide a fine characterization of when polynomial algorithms exist for the above problems, and when these problems become intractable.