The Complexity of Plan Existence and Evaluation in Probabilistic Domains

TL;DR

This paper analyzes the computational complexity of plan existence and evaluation in probabilistic planning, revealing many problems are complete for various complexity classes, highlighting challenges and directions for future AI research.

Contribution

It provides a comprehensive complexity classification for probabilistic planning problems, identifying key classes like PP and NP^PP as particularly significant.

Findings

Many probabilistic planning problems are NP, co-NP, PP, NP^PP, co-NP^PP, or PSPACE complete.

PP and NP^PP classes are especially relevant for AI uncertainty.

Results suggest new directions for algorithm development in probabilistic planning.

Abstract

We examine the computational complexity of testing and finding small plans in probabilistic planning domains with succinct representations. We find that many problems of interest are complete for a variety of complexity classes: NP, co-NP, PP, NP^PP, co-NP^PP, and PSPACE. Of these, the probabilistic classes PP and NP^PP are likely to be of special interest in the field of uncertainty in artificial intelligence and are deserving of additional study. These results suggest a fruitful direction of future algorithmic development.