Mapping Conformant Planning into SAT Through Compilation and Projection

Abstract

Abstract. Conformant planning is a variation of classical AI planning where the initial state is partially known and actions can have nondeterministic effects. While a classical plan must achieve the goal from a given initial state using deterministic actions, a conformant plan must achieve the goal in the presence of uncertainty in the initial state and action effects. Conformant planning is computationally harder than classical planning, and unlike classical planning, cannot be reduced polynomially to SAT (unless P = NP). Current SAT approaches to conformant planning, such as those considered by Giunchiglia and colleagues, thus follow a generate-and-test strategy: the models of the theory are generated one by one using a SAT solver (assuming a given planning horizon), and from each such model, a candidate conformant plan is extracted and tested for validity using another SAT call. This works well when the theory has few candidate plans and models, but otherwise is too inefficient. In this paper we propose a different use of a SAT engine for computing conformant plans where the existence of conformant plans and their extraction is carried out by means of a single SAT call over a transformed theory. This transformed theory is obtained by projecting the original theory over the action variables. This operation, while intractable, can be done efficiently provided that the original theory is compiled into DNNF (Darwiche 2000), a form akin to OBDDs (Bryant 1992). The experiments that are reported show that the resulting compile-project-sat planner is competitive with state-of-the-art optimal conformant planners and improves upon a planner recently reported at ICAPS-05. The techniques apply in direct fashion to the solution of QBFs of the form ∃x ∀y ∃z φ which are in correspondence to the problem of verifying the existence of conformant plans for a given horizon.

Planning with Incomplete Information in Quantified Answer Set Programming

“…2003) is similar to dlv K in identifying a potential plan before validating it. compile-project-sat (Palacios and Geffner 2005) uses a single call to a SAT solver to compute a conformant plan. Their validity check is doable in linear time, if the planning problem is encoded in deterministic decomposable negation normal form.…”

Recent advances in conformant planning

“…As shown in Fig.1, CGP [5] is a modification of Graphplan [20], which enjoys great success in classical planning field. References [27,36] have shown that conformant planning can be compiled into SAT instances and thus be solved by efficient SAT-solvers. Similar ideas can be found in the famous classical planning systems like SATPLAN [37][38][39] and BlackBox [40].…”

“…Cf2sat is an optimal conformant planner presented by Palacios and Geffner [27]. Cf2sat transforms the PDDL into a propositional theory, that is later compiled into normal form called Decomposability and Determinism of Negation Normal Form (d-DNNF) [28][29][30][31] to obtain a new formula that encodes all the possible plans.…”

Propagation complete encodings of smooth DNNF theories

“…There are also approaches that resolve a conflict by extending the instance by clauses that contain auxiliary variables new in the instance by lazily expanding a corresponding part of a large known encoding of the constraint [3,20]. Specific situations, where a CNF encoding of a DNNF is suitable for use in a SAT instance are described in [29,32].…”