Strong-Cyclic Planning when Fairness is Not a Valid Assumption

We address the class of fully-observable nondeterministic (FOND) planning problems where non-deterministic actions are not guaranteed to display fair behaviour. Typical solutions to FOND planning problems either guarantee goal reachability with a bounded number of transitions (so-called strong acyclic solutions), or are predicated on a fairness assumption that presumes each action effect occurs infinitely often when the action is applied infinite times in the same state (so-called strongcyclic solutions). We introduce the FOND planning model, that extends the FOND model with a more informed description of the action transitions. Solutions to FOND problems guarantee goal reachability, even when the classical fairness assumption is not valid. We characterize different topologies, or classes, of solutions showing that typical strong acyclic, and fair strong-cyclic planning are particular cases. Moreover, we characterize a class of FOND solutions that also solve 1primary normative fault-tolerant problems, and are robust to any finite number of faults during execution. We present algorithms to solve each class of problems. Finally, we present the results of one of our algorithms in the search for so-called normative solutions for a selection of blocksworld problems where the classical fairness assumption is not valid.