An Investigation into the Computational Complexity of Planning in Nondeterministic and Information-incomplete Domains Domain-independent Planning

Though the planning problem, including the computational complexity of planning , has been long studied in AI, the problem of planning with incomplete information has recieved relatively little attention. Planning with incomplete information may mean any one of a number of diierent things; It may mean that certain facts of the initial state are not known, that plans may contain sensing operations, or that operators can have probabilistic or nondeterministic eeects. The computational complexity of this problem has been even less investigated. We examine the complexity of contingent planning, constructing plans that will work in every forseable case. Varying restrictions on the operator and state description incompletness, ranging from totaly unconstrained to allowing only incomplete initial state and determinstic contex-independent operators, result in complexities ranging from EXPSPACE-complete to PSPACE-complete, which is also the known complexity of propositional planning with determinism and complete information. The plan synthesis problem or planning problem is a formalised version of the problem given a description of the initial state, the desired goal state (or states) and a set of operators, nd a sequence of operator instances such that the state resulting from execution of the entire sequence is a goal state. Planning is sometimes refered to as domain independent planning, since the domain, as described by the available operators and their eeects, is a part of the problem instance. Even though the problem has been much studied since the beginnings of arti-, the most common formalisation is still the same as was used in the STRIPS system 11]. The STRIPS formalism requires operators to have conjunctive preconditions and deterministic context-independent eeects. A later development, ADL 23], extends STRIPS to incorporate context-dependent eeects and preconditions including limited disjunctions. Both do however represent domains and operators in rst order predicate logic. When the domain contains an innnite number of ground terms, the planning problem becomes undecidable 10]. First order predicate logic over a nite domain of ground terms is equivalent to propositional logic, but allows for more compact encodings. Though most research into the planning problem has focused only on the case of complete information, i.e. when all relevant information about the initial state and the eeects of executing operators is available to the planner, several approaches to dealing with more complex and realistic cases have been presented. These fall roughly in three categories; conditional, contingent and probabilistic 1. In addition, some classical planners can deal with …