Generalized Planning: Synthesizing Plans that Work for Multiple Environments

We give a formal definition of generalized planning that is independent of any representation formalism. We assume that our generalized plans must work on a set of deterministic environments, which are essentially unrelated to each other. We prove that generalized planning for a finite set of environments is always decidable and EXPSPACE-complete. Our proof is constructive and gives us a sound, complete and complexity-wise optimal technique. We also consider infinite sets of environments, and show that generalized planning for the infinite "one-dimensional problems," known in the literature to be recursively enumerable when restricted to finite-state plans, is EXPSPACE-decidable without sequence functions, and solvable by generalized planning for finite sets.

[1]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

[2]  Yuxiao Hu,et al.  A Correctness Result for Reasoning about One-Dimensional Planning Problems , 2010, IJCAI.

[3]  Hector J. Levesque,et al.  Planning with Loops , 2005, IJCAI.

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Cédric Pralet,et al.  Constraint-Based Controller Synthesis in Non-Deterministic and Partially Observable Domains , 2010, ECAI.

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

[7]  Giuseppe De Giacomo,et al.  Automata-Theoretic Approach to Planning for Temporally Extended Goals , 1999, ECP.

[8]  Klaus Weihrauch,et al.  The computational complexity of some julia sets , 2002, STOC '03.

[9]  Neil Immerman,et al.  Learning Generalized Plans Using Abstract Counting , 2008, AAAI.

[10]  Hector Geffner,et al.  A Translation-Based Approach to Contingent Planning , 2009, IJCAI.

[11]  Paolo Traverso,et al.  Automated Planning: Theory & Practice , 2004 .

[12]  Stefan Edelkamp,et al.  Automated Planning: Theory and Practice , 2007, Künstliche Intell..

[13]  Hector Geffner,et al.  Compiling Uncertainty Away in Conformant Planning Problems with Bounded Width , 2009, J. Artif. Intell. Res..

[14]  Jussi Rintanen,et al.  Complexity of Planning with Partial Observability , 2004, ICAPS.

[15]  Nils J. Nilsson,et al.  Artificial Intelligence , 1974, IFIP Congress.

[16]  Blai Bonet,et al.  Automatic Derivation of Memoryless Policies and Finite-State Controllers Using Classical Planners , 2009, ICAPS.

[17]  Patrik Haslum,et al.  Some Results on the Complexity of Planning with Incomplete Information , 1999, ECP.

[18]  Fahiem Bacchus,et al.  Planning for temporally extended goals , 1996, Annals of Mathematics and Artificial Intelligence.

[19]  Yuxiao Hu,et al.  Planning with Loops: Some New Results , 2009 .

[20]  Neil Immerman,et al.  A new representation and associated algorithms for generalized planning , 2011, Artif. Intell..