Optimistic and disjunctive agent design problems

Abstract

The agent design problem is as follows: Given an environment, together with a specification of a task, is it possible to construct an agent that can be guaranteed to successfully accomplish the task in the environment? In previous research, it was shown that for two important classes of tasks (where an agent was required to either achieve some state of affairs or maintain some state of affairs), the agent design problem was PSPACE-complete. In this paper, we consider several important generalisations of such tasks. In an optimistic agent design problem, we simply ask whether an agent has at least some chance of bringing about a goal state. In a combined design problem, an agent is required to achieve some state of affairs while ensuring that some invariant condition is maintained. Finally, in a disjunctive design problem, we are presented with a number of goals and corresponding invariants - the aim is to design an agent that on any given run, will achieve one of the goals while maintaining the corresponding invariant. We prove that while the optimistic achievement and maintenance design problems are NP-complete, the PSPACE-completeness results obtained for achievement and maintenance tasks generalise to combined and disjunctive agent design. © Springer-Verlag Berlin Heidelberg 2001.