Exploiting Macro-actions and Predicting Plan Length in Planning as Satisfiability

The use of automatically learned knowledge for a planning domain can significantly improve the performance of a generic planner when solving a problem in this domain. In this work, we focus on the well-known SAT-based approach to planning and investigate two types of learned knowledge that have not been studied in this planning framework before: macro-actions and planning horizon. Macro-actions are sequences of actions that typically occur in the solution plans, while a planning horizon of a problem is the length of a (possibly optimal) plan solving it. We propose a method that uses a machine learning tool for building a predictive model of the optimal planning horizon, and variants of the well-known planner SatPlan and solver MiniSat that can exploit macro actions and learned planning horizons to improve their performance. An experimental analysis illustrates the effectiveness of the proposed techniques

The Complexity of Reasoning with FODD and GFODD

Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a knowledge representation that is useful in mechanizing decision theoretic planning in relational domains. GFODDs generalize function-free first order logic and include numerical values and numerical generalizations of existential and universal quantification. Previous work presented heuristic inference algorithms for GFODDs and implemented these heuristics in systems for decision theoretic planning. In this paper, we study the complexity of the computational problems addressed by such implementations. In particular, we study the evaluation problem, the satisfiability problem, and the equivalence problem for GFODDs under the assumption that the size of the intended model is given with the problem, a restriction that guarantees decidability. Our results provide a complete characterization placing these problems within the polynomial hierarchy. The same characterization applies to the corresponding restriction of problems in first order logic, giving an interesting new avenue for efficient inference when the number of objects is bounded. Our results show that for $\Sigma_k$ formulas, and for corresponding GFODDs, evaluation and satisfiability are $\Sigma_k^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete. For $\Pi_k$ formulas evaluation is $\Pi_k^p$ complete, satisfiability is one level higher and is $\Sigma_{k+1}^p$ complete, and equivalence is $\Pi_{k+1}^p$ complete.Comment: A short version of this paper appears in AAAI 2014. Version 2 includes a reorganization and some expanded proof

LTLf satisfiability checking

We consider here Linear Temporal Logic (LTL) formulas interpreted over \emph{finite} traces. We denote this logic by LTLf. The existing approach for LTLf satisfiability checking is based on a reduction to standard LTL satisfiability checking. We describe here a novel direct approach to LTLf satisfiability checking, where we take advantage of the difference in the semantics between LTL and LTLf. While LTL satisfiability checking requires finding a \emph{fair cycle} in an appropriate transition system, here we need to search only for a finite trace. This enables us to introduce specialized heuristics, where we also exploit recent progress in Boolean SAT solving. We have implemented our approach in a prototype tool and experiments show that our approach outperforms existing approaches

Towards compositional automated planning

The development of efficient propositional satisfiability problem solving algorithms (SAT solvers) in the past two decades has made automated planning using SAT-solvers\ua0an established AI planning approach. Modern SAT solvers can\ua0accommodate a wide variety of planning problems with a large number of variables. However, fast computing of reasonably long\ua0plans proves challenging for planning as satisfiability. In order to address this challenge, we present a compositional approach based on abstraction refinement that iteratively generates, solves and composes partial solutions from a parameterized planning problem. We show that this approach decomposes the monolithic planning problem into smaller problems and thus significantly speeds up plan calculation, at least for a class of tested planning problems