The Complexity of Plan Existence and Evaluation in Probabilistic Domains

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, NPPP, co-NP PP, and PSPACE. Of these, the probabilistic classes PP and NPPP 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.

[1]  Hermann Jung.  On Probabilistic Time and Space , 1985, ICALP.

[2]  David Chapman,et al.  Planning for Conjunctive Goals , 1987, Artif. Intell..

[3]  John N. Tsitsiklis,et al.  The Complexity of Markov Decision Processes , 1987, Math. Oper. Res..

[4]  Richard E. Ladner.  Polynomial Space Counting Problems , 1989, SIAM J. Comput..

[5]  David A. McAllester,et al.  Systematic Nonlinear Planning , 1991, AAAI.

[6]  Christer Bäckström,et al.  Planning in polynomial time: the SAS‐PUBS class , 1991, Comput. Intell..

[7]  Seinosuke Toda,et al.  PP is as Hard as the Polynomial-Time Hierarchy , 1991, SIAM J. Comput..

[8]  J. Tor,et al.  Complexity classesde ned by counting quanti ers * , 1991 .

[9]  Anne Condon,et al.  The Complexity of Stochastic Games , 1992, Inf. Comput..

[10]  Carme Àlvarez,et al.  A Very Hard log-Space Counting Class , 1993, Theor. Comput. Sci..

[11]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[12]  Daniel S. Weld,et al.  Probabilistic Planning with Information Gathering and Contingent Execution , 1994, AIPS.

[13]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[14]  Eric Allender,et al.  Relationships among PL, #L, and the determinant , 1994, Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory.

[15]  Tom Bylander,et al.  The Computational Complexity of Propositional STRIPS Planning , 1994, Artif. Intell..

[16]  Nicholas Kushmerick,et al.  An Algorithm for Probabilistic Planning , 1995, Artif. Intell..

[17]  David E. Smith,et al.  Representation and Evaluation of Plans with Loops , 1995 .

[18]  Avrim Blum,et al.  Fast Planning Through Planning Graph Analysis , 1995, IJCAI.

[19]  V. S. Subrahmanian,et al.  Complexity, Decidability and Undecidability Results for Domain-Independent Planning , 1995, Artif. Intell..

[20]  Craig Boutilier,et al.  Exploiting Structure in Policy Construction , 1995, IJCAI.

[21]  Christopher Lusena,et al.  The Complexity of Deterministically Observable Finite-horizon Markov Decision Processes , 1996 .

[22]  Michael L. Littman,et al.  Algorithms for Sequential Decision Making , 1996 .

[23]  T. Dean,et al.  Generating optimal policies for high-level plans with conditional branches and loops , 1996 .

[24]  E. Allender,et al.  The Complexity of Unobservable Nite-horizon Markov Decision Processes , 1996 .

[25]  T. Dean,et al.  Planning under uncertainty: structural assumptions and computational leverage , 1996 .

[26]  Craig Boutilier,et al.  Abstraction and Approximate Decision-Theoretic Planning , 1997, Artif. Intell..

[27]  Michael L. Littman,et al.  Probabilistic Propositional Planning: Representations and Complexity , 1997, AAAI/IAAI.

[28]  Leslie Pack Kaelbling,et al.  Planning and Acting in Partially Observable Stochastic Domains , 1998, Artif. Intell..

[29]  Jacobo Torr.  Complexity Classes Deened by Counting Quantiiers* , 2022 .