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68
The Computational Complexity of Propositional STRIPS Planning
 Artificial Intelligence
, 1994
"... I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation ..."
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Cited by 299 (3 self)
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I present several computational complexity results for propositional STRIPS planning, i.e., STRIPS planning restricted to ground formulas. Different planning problems can be defined by restricting the type of formulas, placing limits on the number of pre and postconditions, by restricting negation in pre and postconditions, and by requiring optimal plans. For these types of restrictions, I show when planning is tractable (polynomial) and intractable (NPhard) . In general, it is PSPACEcomplete to determine if a given planning instance has any solutions. Extremely severe restrictions on both the operators and the formulas are required to guarantee polynomial time or even NPcompleteness. For example, when only ground literals are permitted, determining plan existence is PSPACEcomplete even if operators are limited to two preconditions and two postconditions. When definite Horn ground formulas are permitted, determining plan existence is PSPACEcomplete even if operators are limited t...
An Algorithm for Probabilistic Planning
, 1995
"... We define the probabilistic planning problem in terms of a probability distribution over initial world states, a boolean combination of propositions representing the goal, a probability threshold, and actions whose effects depend on the executiontime state of the world and on random chance. Adoptin ..."
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Cited by 258 (18 self)
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We define the probabilistic planning problem in terms of a probability distribution over initial world states, a boolean combination of propositions representing the goal, a probability threshold, and actions whose effects depend on the executiontime state of the world and on random chance. Adopting a probabilistic model complicates the definition of plan success: instead of demanding a plan that provably achieves the goal, we seek plans whose probability of success exceeds the threshold. In this paper, we present buridan, an implemented leastcommitment planner that solves problems of this form. We prove that the algorithm is both sound and complete. We then explore buridan's efficiency by contrasting four algorithms for plan evaluation, using a combination of analytic methods and empirical experiments. We also describe the interplay between generating plans and evaluating them, and discuss the role of search control in probabilistic planning. 3 We gratefully acknowledge the comment...
Temporal Reasoning Based on SemiIntervals
, 1992
"... A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledg ..."
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Cited by 234 (14 self)
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A generalization of Allen's intervalbased approach to temporal reasoning is presented. The notion of `conceptual neighborhood' of qualitative relations between events is central to the presented approach. Relations between semiintervals rather than intervals are used as the basic units of knowledge. Semiintervals correspond to temporal beginnings or endings of events. We demonstrate the advantages of reasoning on the basis of semiintervals: 1) semiintervals are rather natural entities both from a cognitive and from a computational point of view; 2) coarse knowledge can be processed directly; computational effort is saved; 3) incomplete knowledge about events can be fully exploited; 4) incomplete inferences made on the basis of complete knowledge can be used directly for further inference steps; 5) there is no tradeoff in computational strength for the added flexibility and efficiency; 6) for a natural subset of Allen's algebra, global consistency can be guaranteed in polynomial time; 7) knowledge about relations between events can be represented much more compactly.
Complexity Results for SAS+ Planning
 COMPUTATIONAL INTELLIGENCE
, 1993
"... We have previously reported a number of tractable planning problems defined in the SAS+ formalism. This report complements these results by providing a complete map over the complexity of SAS+ planning under all combinations of the previously considered restrictions. We analyze the complexity ..."
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Cited by 149 (24 self)
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We have previously reported a number of tractable planning problems defined in the SAS+ formalism. This report complements these results by providing a complete map over the complexity of SAS+ planning under all combinations of the previously considered restrictions. We analyze the complexity both of finding a minimal plan and of finding any plan. In contrast to other complexity surveys of planning we study not only the complexity of the decision problems but also of the generation problems. We prove that the SAS+PUS problem is the maximal tractable problem under the restrictions we have considered if we want to generate minimal plans. If we are satisfied with any plan, then we can generalize further to the SAS+US problem, which we prove to be the maximal tractable problem in this case.
Complexity, Decidability and Undecidability Results for DomainIndependent Planning
 ARTIFICIAL INTELLIGENCE
, 1995
"... In this paper, we examine how the complexity of domainindependent planning with STRIPSstyle operators depends on the nature of the planning operators. We show ..."
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Cited by 134 (25 self)
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In this paper, we examine how the complexity of domainindependent planning with STRIPSstyle operators depends on the nature of the planning operators. We show
Supporting ValidTime Indeterminacy
 ACM Transactions on Database Systems
, 1998
"... In validtime indeterminacy it is known that an event stored in a database did in fact occur, but it is not known exactly when. In this paper we extend the SQL data model and query language to support validtime indeterminacy. We represent the occurrence time of an event with a set of possible insta ..."
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Cited by 86 (17 self)
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In validtime indeterminacy it is known that an event stored in a database did in fact occur, but it is not known exactly when. In this paper we extend the SQL data model and query language to support validtime indeterminacy. We represent the occurrence time of an event with a set of possible instants, delimiting when the event might have occurred, and a probability distribution over that set. We also describe query language constructs to retrieve information in the presence of indeterminacy. These constructs enable users to specify their credibility in the underlying data and their plausibility in the relationships among that data. A denotational semantics for SQL’s select statement with optional credibility and plausibility constructs is given. We show that this semantics is reliable, in that it never produces incorrect information, is maximal, in that if it were extended to be more informative, the results may not be reliable, and reduces to the previous semantics when there is no indeterminacy. Although the extended data model and query language provide needed modeling capabilities, these extensions appear initially to carry a significant execution cost. A contribution of this paper is to demonstrate that our approach is useful and practical. An efficient representation of validtime indeterminacy and efficient query processing algorithms are provided. The cost of
Qualitative and Quantitative Simulation: Bridging the Gap
 Artificial Intelligence
, 1997
"... Shortcomings of qualitative simulation and of quantitative simulation motivate combining them to do simulations exhibiting strengths of both. The resulting class of techniques is called semiquantitative simulation. One approach to semiquantitative simulation is to use numeric intervals to represe ..."
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Cited by 43 (1 self)
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Shortcomings of qualitative simulation and of quantitative simulation motivate combining them to do simulations exhibiting strengths of both. The resulting class of techniques is called semiquantitative simulation. One approach to semiquantitative simulation is to use numeric intervals to represent incomplete quantitative information. In this research we demonstrate semiquantitative simulation using intervals in an implemented semiquantitative simulator called Q3. Q3 progressively refines a qualitative simulation, providing increasingly specific quantitative predictions which can converge to a numerical simulation in the limit while retaining important correctness guarantees from qualitative and interval simulation techniques. Q3's simulations are based on a technique we call step size refinement. While a pure qualitative simulation has a very coarse step size, representing the state of a system trajectory at relatively few qualitatively distinct states, Q3 interpolates newly expl...
Modeling a Dynamic and Uncertain World I: Symbolic and Probabilistic Reasoning about Change
 Artificial Intelligence
, 1993
"... Intelligent agency requires some ability to predict the future. An agent must ask itself what is presently its best course of action given what it now knows about what the world will be like when it intends to act. This paper presents a system that uses a probabilistic model to reason about the effe ..."
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Cited by 41 (7 self)
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Intelligent agency requires some ability to predict the future. An agent must ask itself what is presently its best course of action given what it now knows about what the world will be like when it intends to act. This paper presents a system that uses a probabilistic model to reason about the effects of an agent's proposed actions on a dynamic and uncertain world, computing the probability that relevant propositions will hold at a specified point in time. The model allows for incomplete information about the world, the occurrence of exogenous (unplanned) events, unreliable sensors, and the possibility of an imperfect causal theory. The system provides an application program with answers to questions of the form "is the probability that ' will hold in the world at time t greater than ø ?" It is unique among algorithms for probabilistic temporal reasoning in that it tries to limit its inference according to the proposition, time, and probability threshold provided by the application. T...
Commitment Strategies in Planning: A Comparative Analysis
 In Proceedings of IJCAI91
, 1991
"... In this paper we compare the utility of different commitment strategies in planning. Under a "least commitment strategy", plans are represented as partial orders and operators are ordered only when interactions are detected. We investigate claims of the inherent advantages of planning with ..."
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Cited by 40 (1 self)
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In this paper we compare the utility of different commitment strategies in planning. Under a "least commitment strategy", plans are represented as partial orders and operators are ordered only when interactions are detected. We investigate claims of the inherent advantages of planning with partial orders, as compared to planning with total orders. By focusing our analysis on the issue of operator ordering commitment, we are able to carry out a rigorous comparative analysis of two planners. We show that partialorder planning can be more efficient than totalorder planning, but we also show that this is not necessarily so. 1
Statevariable planning under structural restrictions: Algorithms and complexity
 ARTIFICIAL INTELLIGENCE
, 1998
"... Computationally tractable planning problems reported in the literature so far have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying statetransition grap ..."
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Cited by 39 (3 self)
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Computationally tractable planning problems reported in the literature so far have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying statetransition graph. The exponential size of this graph, though, makes such restrictions costly to test. Hence, we propose an intermediate approach, using a state variable model for planning and defining restrictions on the separate statetransition graphs for each state variable. We identify such restrictions which can tractably be tested and we present a planning algorithm which is correct and runs in polynomial time under these restrictions. The algorithm has been implemented an it outperforms Graphplan on a number of test instances. In addition, we present an exhaustive map of the complexity results for planning under all combinations of four previously studied syntactical restrictions and our five new structural restrictions. This complexity map considers both the optimal and nonoptimal plan generation problem.