Peter Jonsson

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Computationally tractable planning problems reported in the literature so far have almost exclusively been de ned by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying state-transition graph. The exponential size of this graph, though, makes such(More)
We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satis ability problem for RCC-5 is known to be NP-complete but not much is known about its approximately four billion subclasses. We provide a complete classi cation of satis ability for all these subclasses(More)
We present a class, 3S, of planning instances such that the plan existence problem is tractable while plan generation is provably intractable for instances of this class. The class is defined by simple structural restrictions, all of them testable in polynomial‐time. Furthermore, we show that plan generation can be carried out in time bounded by a(More)
Allen's interval algebra is one of the best established formalisms for temporal reasoning. This article provides the final step in the classification of complexity for satisfiability problems over constraints expressed in this algebra. When the constraints are chosen from the full Allen's algebra, this form of satisfiability problem is known to be(More)
We present a formalism, Disjunctive Linear Relations (DLRs), for reasoning about temporal constraints. DLRs subsume most of the formalisms for temporal constraint reasoning proposed in the literature and is therefore computationally expensive. We also present a restricted type of DLRs, Horn DLRs, which have a polynomial-time satissability problem. We prove(More)
For every class of relational structures C, let HOM(C, _) be the problem of deciding whether a structure A ∈ C has a homomorphism to a given arbitrary structure B. Grohe has proved that, under a certain complexity-theoretic assumption, HOM(C, _) is solvable in polynomial time if and only if the cores of all structures in C have bounded tree-width. We prove(More)
Classical propositional STRIPS planning is nothing but the search for a path in the state-transition graph induced by the operators in the planning problem. What makes the problem hard is the size and the sometimes adverse structure of this graph. We conjecture that the search for a plan would be more efficient if there were only a small number of paths(More)