144 research outputs found
Universal First-Order Logic is Superfluous for NL, P, NP and coNP
In this work we continue the syntactic study of completeness that began with
the works of Immerman and Medina. In particular, we take a conjecture raised by
Medina in his dissertation that says if a conjunction of a second-order and a
first-order sentences defines an NP-complete problems via fops, then it must be
the case that the second-order conjoint alone also defines a NP-complete
problem. Although this claim looks very plausible and intuitive, currently we
cannot provide a definite answer for it. However, we can solve in the
affirmative a weaker claim that says that all ``consistent'' universal
first-order sentences can be safely eliminated without the fear of losing
completeness. Our methods are quite general and can be applied to complexity
classes other than NP (in this paper: to NLSPACE, PTIME, and coNP), provided
the class has a complete problem satisfying a certain combinatorial property
Conformant plans and beyond: Principles and complexity
AbstractConformant planning is used to refer to planning for unobservable problems whose solutions, like classical planning, are linear sequences of operators called linear plans. The term ‘conformant’ is automatically associated with both the unobservable planning model and with linear plans, mainly because the only possible solutions for unobservable problems are linear plans. In this paper we show that linear plans are not only meaningful for unobservable problems but also for partially-observable problems. In such case, the execution of a linear plan generates observations from the environment which must be collected by the agent during the execution of the plan and used at the end in order to determine whether the goal had been achieved or not; this is the typical case in problems of diagnosis in which all the actions are knowledge-gathering actions.Thus, there are substantial differences about linear plans for the case of unobservable or fully-observable problems, and for the case of partially-observable problems: while linear plans for the former model must conform with properties in state space, linear plans for partially-observable problems must conform with properties in belief space. This differences surface when the problems are allowed to express epistemic goals and conditions using modal logic, and place the plan-existence decision problem in different complexity classes.Linear plans is one extreme point in a discrete spectrum of solution forms for planning problems. The other extreme point is contingent plans in which there is a branch point for every possible observation at each time step, and thus the number of branch points is not bounded a priori. In the middle of the spectrum, there are plans with a bounded number of branch points. Thus, linear plans are plans with zero branch points and contingent plans are plans with unbounded number of branch points.In this work, we lay down foundations and principles for the general treatment of linear plans and plans of bounded branching, and provide exact complexity results for novel decision problems. We also show that linear plans for partially-observable problems are not only of theoretical interest since some challenging real-life problems can be dealt with them
Learning Features and Abstract Actions for Computing Generalized Plans
Generalized planning is concerned with the computation of plans that solve
not one but multiple instances of a planning domain. Recently, it has been
shown that generalized plans can be expressed as mappings of feature values
into actions, and that they can often be computed with fully observable
non-deterministic (FOND) planners. The actions in such plans, however, are not
the actions in the instances themselves, which are not necessarily common to
other instances, but abstract actions that are defined on a set of common
features. The formulation assumes that the features and the abstract actions
are given. In this work, we address this limitation by showing how to learn
them automatically. The resulting account of generalized planning combines
learning and planning in a novel way: a learner, based on a Max SAT
formulation, yields the features and abstract actions from sampled state
transitions, and a FOND planner uses this information, suitably transformed, to
produce the general plans. Correctness guarantees are given and experimental
results on several domains are reported.Comment: Preprint of paper accepted at AAAI'19 conferenc
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