We study the consequences on complexity that arise when bounds on the number of branch points on the solutions for non-deterministic planning problems are imposed as well as when modal formulae are introduced into the description language. New planning tasks, such as whether there exists a plan with at most k branch points for a fully (or partially) observable non-deterministic domain, and whether there exists a no-branch (a.k.a. conformant) plan for partially observable domains, are introduced and their complexity analyzed. Among other things, we show that deciding the existence of a conformant plan for partially observable domains with modal formulae is 2EXPSPACE-complete, and that the problem of deciding the existence of plans with bounded branching, for fully or partially observable contingent domains, has the same complexity of the conformant task. These results generalize previous results on the complexity of non-deterministic planning and fill a slot that has gone unnoticed in non-deterministic planning, that of conformant planning for partially observable domains.
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