Knoblock, C. A. (1994a). Automatically generating abstractions for planning. Artificial Intelligence, 68 (2), 243--302.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....only a planning algorithm but also procedures for learning and case based reasoning, which greatly increase the efficiency of the planner. For example, Prodigy is able to learn control rules [Minton, 1988] conduct experiments to acquire new knowledge [Gil, 1992] generate abstraction hierarchies [Knoblock, 1993], and use andlogical reasoning to recognize and exploit similarities between planning problems [Veloso, 1992] Prodigy s core, the planning algorithm itself, has been improved over the years. The old algorithm, Prodigy2.0 [Minton et al. 1989] was succeeded by NoLimit [Veloso, 1989] and then by ....

Craig Knoblock. Automatically Generating Abstractions for Planning. Ar- tificial Intelligence, 1993, in press.

....one another, or should only interact in limited ways. Fortunately, many domains and applications do benefit from decomposable solution structures, as is evident from the popularity of hierarchical problem solving and decompositional design techniques in general (see, for example, 2] 4] 6] [14], 16] 17] 36] 37] 8 RELATED WORK Hierarchical case based reasoning is one way of supporting multiple case reuse. Its distinguishing features include: 1) Using cases at multiple levels of abstraction to represent complex problem solutions as hierarchies; 2) Using abstract case solutions ....

C. Knoblock, "Automatically Generating Abstractions for Planning, " Artificial Intelligence, vol. 64, 1994.

....is performed, many rules are generated that give all the cases when the heuristic has underestimated the number of moves. Out of all this rules, the most simple and general can be kept. A similar method to generate admissible heuristics is to remove conditions inside the rules of the game [11, 12]. The two methods overlap, but a combination of the two might give better results than each of them. 7 Conclusion and Future Work We have given experimental evidence that admissible heuristics on moves in two player games account for a large speed up for threat search algorithms. These ....

Knoblock, C.A.: Automatically generating abstractions for planning. Arti cial Intelligence 68 (1994) 243-302

....of the world given at a lower level of detail. The most significant forms of state based abstraction rely on (i) relaxed models, obtained by dropping operators applicability conditions [10] and on (ii) reduced models, obtained by completely removing certain conditions from the problem space [6]. Both models, while preserving the provability of plans that hold at the ground level, perform a weakening of the original problem space, thus suffering from the drawback of introducing false solutions at the abstract levels [4] Analysis and experiments have shown that hierarchical planning ....

....disregarded, being assumed by default. However, for the sake of clarity, a knowledge engineer may explicitly state which predicates should not be translated upward according to the given syntax. Let us point out that the translations described above allow specifying Knoblock s reduced models [6], although the expressive power of such notation is not limited to a simple on off translation. In general, is a and part of abstractions performed over types and or predicates are feasible, too. Nevertheless, how to deal with such extensions is still an open problem, as several drawbacks ....

Knoblock, C.A., Automatically Generating Abstractions for Planning, Artificial Intelligence, 68:2 (1994) 243--302.

....using an abstraction space, formed by dropping information, it is dicult to guarantee that if there exists an abstract solution, there exists also a solution in the base space. This problem is called the false proof problem [84, 31] 2.4. 1 Generating abstraction hierarchies We use Knoblock s [57] algorithm designed for STRIPS like operators (representable by sequents in LL sequent calculus) to generate abstraction hierarchies with major adjustment that antecedents of LL sequents represent preconditions and succedents take the role of e ects in Knoblock s terminology. To suit LL program ....

....of abstraction new concurrent fragments may be found. Anyway, the abstraction hierarchy determines the ordering of these concurrent executions by means of expected program context in the end of execution of a concurrent fragment. 2.4. 5 The computational complexity of abstraction According to [57] the complexity of building the constraint graph is O(n o l ) where n is the number of di erent literals in a LL program, o is the maximum number of LL program clauses relevant for achieving any given literal, and l is the length of the succedent (total number of di erent literals in ....

C. A. Knoblock. Automatically generating abstractions for planning. Arti- cial Intelligence, Vol. 68, pp. 243-302, 1994.

....exponential symbol in a clause means that the particular clause may be used an arbitrary number of times. To allow shorter representation of formulae, we are using in the following sometime abbreviation a = for n 0. 2 Generating abstraction hierarchies We use Knoblock s [8] algorithm designed for STRIPS like operators (representable by sequents in LL sequent calculus) to generate abstraction hierarchies with the major adjustment that the antecedents of LL sequents represent preconditions and succedents take the role of e ects in Knoblock s terminology. To suit LL ....

.... means inserting new branches into a proof tree. The main e ect of abstraction is eliminating inessential program clauses at every abstraction level and thus slicing the original search space into smaller, sequentially searchable ones. 5 The computational complexity of abstraction According to [8] the complexity of building the constraint graph is O(n o l ) where n is the number of di erent literals in a LL sequent, o is the maximum number of LL axioms relevant for achieving any given literal, and l is the total number of di erent literals in succedents of relevant axioms. Building ....

C. A. Knoblock. Automatically generating abstractions for planning. Arti cial Intelligence, 68:243-302, 1994.

....and the disadvantage of a highly restricted horizon. Just the opposite holds for long term planning. To adjust the agent s planning horizon properly, we are experimenting with layered planning, which tries to incorporate the advantages of both reactivity and planning (related to abstractions [10, 16] and Hierarchical Task Network (HTN) planning [5, 15] Figure 2 shows the different layers of planning, which include coarse grained planning on the intention layer, fine grained planning on the skill layer and execution on the atomic actions layer. Following the principle of decomposed ....

Knoblock, C. A.: Automatically generating Abstractions for Planning. Artificial Intelligence 68(2). 1994.

.... consult simpli ed models of the problem domain [4, 5, 11, 13] These simpli ed models are generated via constraint deletion, i.e. ignoring selected constraints on the applicability of operators. Recently, there has been renewed interest in this and other uses of abstraction in problem solving [9, 10, 12, 15], including a generalization of the notion of simpli cation [14] that will be described below. Pearl [13] discusses the use of constraint deletion to generate three known heuristics for the familiar Eight Puzzle problem. He formalizes the problem in terms of domain predicates, and then describes ....

C. A. Knoblock. Automatically Generating Abstractions for Planning. In Proceedings of the International Workshop on Change of Representation and Inductive Bias, Philips Laboratories, Briarcli Manor, New York, 1988.

....hierarchical planning, approximate methods, problem coordination, constraint programming, formal models. 1 2 PER KREUGER, MARTIN ARONSSON, SIMON LINDBLOM 1. Introduction Abstraction as mechanism to simplify complex planning problems have been studied in arti cial intelligence [Yan97, Kno94] However as a heuristic to solve scheduling and resource allocation problems we have not so far seen any general mechanism described in the literature. The authors of [CLS99] describe an approach to automatically generate meta heuristics using a particular notion of abstraction but do not ....

C Knoblock. Automatically generating abstractions for planning. Articial Intelligence, 68(2):243302, 1994.

....of the world given at a lower level of detail. The most significant forms of state based abstraction rely on: i) relaxed models, obtained by dropping operators applicability conditions [15] and on (ii) reduced models, obtained by completely removing certain conditions from the problem space [8]. Both models, while preserving the provability of plans that hold at the ground level, perform a weakening of the original problem space, thus suffering from the problem of introducing false solutions at the abstract level [5] Given a problem space and a set of abstraction spaces organized in ....

.... learning control knowledge have been proposed; in particular, let us recall: a) learning abstractions from the domain knowledge (e.g. ABSTRIPS [15] b) learning macro operators [9] c) explanationbased learning techniques [7] d) learning abstractions from the problem to be solved (e.g. ALPINE [8]) Perhaps, the two most important examples of full integration between learning and planning are the SOAR [11] and PRODIGY [4] systems, where the capability of embedding the learning activity within an adaptive framework that encompasses planning, learning, and execution is experimented. 1.4. ....

C. A. Knoblock, Automatically Generating Abstractions for Planning, Artificial Intelligence, Vol. 68(2), 1994.

....method applies the selected actions as early as possible; we call it apply. The second method uses the same control rules, along with a special rule that delays the application and forces more emphasis on backward search [ Veloso and Stone, 1995 ] we call it delay. The third method, alpine [ Knoblock, 1994 ] is a combination of apply with an abstraction generator, which determines relative importance of domain elements. alpine first ignores the less important elements and builds a solution outline; it then refines the solution, taking care of the initially ignored details. Experiments have shown ....

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243--302, 1994. 35

....rst. This can be done without giving up completeness by stepwise adding actions to the transition relation, which seem heuristically relevant for reaching the goal, and explore the subtrees of the search space generated by these actions rst. This concept is similar to abstraction in planning (Knoblock 1994) and is topic of future research. It should be noted that although we have presented our algorithm in such a way that there is only a single initial state (i.e. the set Z 0 is unitary) the algorithm itself is not restricted to this case. If the initial situation is only incompletely speci ed ....

Knoblock, C. A. 1994. Automatically generating abstractions for planning. Articial Intelligence 68(2).

....subset which contains all states which don t occur at lower levels of the search tree) until there is a goal state among the states encoded. But we anticipate deviations from that pattern by imposing restrictions on uents and actions taken into account (similar to abstraction in planning, e.g. (Knoblock 1994)) The algorithm is similar to Graphplan (Blum Furst 1997) in that it builds up a data structure for each level, which describes the states reachable after the execution of n actions. Unlike Graphplan, that gives only an upper bound of the the set of states reachable by its mutex mechanism, our ....

Knoblock, C. A. 1994. Automatically generating abstractions for planning. Articial Intelligence 68(2).

....is a directed graph whose nodes are the domain propositions. An edge (p; q) appears in the causal graph iff some operator that changes the value of q has a prevail condition (i.e. a precondition that is not affected by the operator) involving p. This problem structure was introduces by Knoblock [15] in the context of automatic generating abstractions for planning. Subsequently, in [13] Jonsson and Backstrom introduced the 3S class of planning problems with unary operators, which was characterized by the acyclicity of the causal graph, and some restrictions on the operator set. It was shown ....

C. Knoblock. Automatically Generating Abstractions for Planning. Artificial Intelligence, 68(2):243--302, 1994.

....no such solution exists. 3 The 3S Class We begin by defining dependency graphs on planning instances. Such a graph represents for each atom p, which other atoms we will possibly have to add or delete in order to add or delete p. The idea is not new; a more restricted variant is used by Knoblock [12] in his Alpine system. From now on, let Pi = hP ; O; s 0 ; hs ; s Gamma ii be an arbitrarily chosen PSN instance. Definition 3.1 Let p 2 P and let Q P . Then, Affects(p) fo 2 O j p 2 add(o) or p 2 del(o)g and Affects(Q) S q2Q Affects(q) 3 Definition 3.2 Define the dependency ....

....tackling non13 tractable classes of planning problems, while also making replanning feasible. The variable graph approach is an obvious continuation of our research into structural restrictions [10] Interestingly, these graphs can be viewed as a generalization of the dependency graphs Knoblock [12] uses for generating abstraction hierarchies, where our graphs contain more information. In earlier publications [4] we have argued that planning problems allowing exponential size optimal solutions should be considered unrealistic. 1 This does not imply that the 3S class is unrealistic, ....

C. A. Knoblock, Automatically generating abstractions for planning, Artif. Intell., 68 (1994) 243--302. 16

....Moreover, hierarchical structures favour the use of hierarchical planners: Different levels in the hierarchy can be viewed as different abstractions of a problem space. Hierarchies of abstraction are known to reduce the size of the search space and, consequently, the complexity in problem solving [16]. Coordination and communication costs are also reduced as horizontal communication (communication among agents at the same level of the hierarchy) is avoided and vertical communication is restricted to comply with the principles of relevance, timeliness, and completeness [7] Even though there ....

C.A. Knoblock. Automatically Generating Abstractions for Planning. Artificial Intelligence, 68:243--302, 1994.

....and learning capabilities over several components of the overall system so these components conduct their planning and learning activities in parallel. Hierarchical distributed problem solving reduces the size of the search space and, consequently, the complexity in problem solving even further [23, 29]. Hierarchical distributed problem solving relies on a hierarchy of abstract problem spaces to focus the search process. Different levels in the hierarchy can be viewed as different abstractions of a problem space. It seems thus that a suitable coordination mechanism for application domains such ....

C.A. Knoblock. Automatically Generating Abstractions for Planning. Artificial Intelligence, 68:243--302, 1994.

....is the possible use of rule based learning techniques for acquiring control knowledge automatically by training the planner on a sequence of smaller problems. Learning of control knowledge has been explored previously for other, more procedural, planners. See, for example, Etzioni (1993) Knoblock (1994), Minton (1988) and Veloso (1992) We are currently exploring forms of control rule learning in our declarative constraint based framework. Acknowledgements We thank Fahiem Bacchus, Carla Gomes, Dana Nau, and Dan Weld for many useful comments and suggestions. The second author received support ....

Knoblock, C. (1994). Automatically generating abstractions for planning. Artificial Intelligence 68(2).

....that can ease the difficult of planning. There are a variety of mechanisms that can be used to exploit structure so as to make planning easier. Abstraction and the related use of hierarchical task network (HTN) planners have been studied in the literature and utilized in planning systems [36, 48, 62, 55], also mechanisms for search control have received much attention. Truly effective planners will probably utilize a number of mechanisms. Hence, it is important that each of these mechanisms be developed and understood. This paper makes a contribution to the development of mechanisms for search ....

....descriptions (in conjunction, perhaps, with the initial 72 state) So an important area for future research will be to employ learning and reasoning techniques to automatically generate this domain specific knowledge. There is a considerable body of work that can be built on in this area, e.g. [42, 36, 22, 45]. The work by McDermott [40] and Bonet et al. 14] can also be viewed in this light. In these works search heuristics are computed dynamically during search. These heuristics try to estimate whether or not the search is making progress towards the goal. Potentially, similar ideas could be used for ....

Craig Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

....good approximations of optimal plans. 113 1 Introduction One common approach to improving the efficiency of planning is to use a hierarchical planner based on state abstraction ignoring certain literals, either in the operator preconditions [ Sacerdoti, 1974 ] or in the whole language [ Knoblock, 1991, 1994 ] First an abstracted version of the problem instance is solved, thus not taking all details into account and resulting in a plan which is correct at this abstraction level. This plan is then used as a skeleton plan to be filled in with more detail at the next lower level a process referred ....

....original, non abstract problem. Although state abstraction cannot avoid exponential search spaces in the general case, it is usually considered a powerful method for reducing the search effort. It has been demonstrated that the method speeds up planning considerably for certain test examples [ Knoblock, 1994; Bacchus and Yang, 1994 ] This is augmented with theoretical results [ Knoblock, 1991 ] showing that state abstraction can reduce the size of the search space from exponential to linear under certain ideal conditions. These conditions are very restrictive, however, and are not likely to be met ....

[Article contains additional citation context not shown here]

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243--302, 1994.

....shown that AbStrips was more efficient than Strips on a number of test examples, but no formal analysis was done of how and if the efficiency was affected. Other well known systems using hierarchical abstraction are Pablo [ Christensen, 1990 ] Abtweak [ Yang and Tenenberg, 1990 ] and Prodigy [ Knoblock, 1994 ] Observe that the idea of hierarchical abstraction can be combined with both standard operator search and HTN planning, as well as with deductive planning. Hierarchical abstraction has been analyzed by, for example, Knoblock [ Knoblock, 1991b ] Knoblock tried to characterize under which ....

....new instances is then solved and its solution constitutes a skeleton to be filled in by solving subproblems from the second instance. This process is referred to as interweaving and can be viewed as a restricted variant of the more general concept refinement, as used in hierarchical abstraction [ Knoblock, 1994 ] In fact, the whole method we use can be viewed as a variant of two level abstraction. However, while hierarchical abstraction is a general method which is not formally well understood it can at some occasions speed up planning considerably [ Knoblock, 1991b ] and at other occasions be ....

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243--302, 1994.

....in the O Plan work) 7 Related work Our work can be seen as abstraction of resources from planning phase. From this angle, our idea of keeping the structure of the causal plan intact during resource allocation phase is akin to the enforcement of ordered monotonicity property in ALPINE[9]. An important difference however is that our work is not dependent on the availability of strong abstractions, but is rather motivated by the desire to exploit the loose coupling between planning and scheduling in most real world domains. If the abstract plan cannot be scheduled, we support ....

Knoblock, C. A. 1994. Automatically Generating Abstractions for Planning. AI Journal, 68(2).

....could be adjusted to balance risk against number of cases. One could limit the coverage to interactions above a given strength threshold. This metric would extend on prior work on detecting goal interactions in planners to improve up the planning search, such as STATIC (Etzioni 1993) Alpine (Knoblock 1994) and Universal Plans (Schoppers 1987) STATIC generates a problem solving graph from the constraints and identifies search control rules for avoiding goal interactions. Alpine identifies interactions to find non interacting sub problems, and universal plans (Schoppers 87) derive reactive control ....

Knoblock, C. 1994. Automatically generating abstractions for planning. Artificial Intelligence 68(2).

....average difference between the two systems is zero. However, 13 both of our tests can be used as indirect evidence for an average speedup hypothesis. While we hope that other researchers will use our tests to validate their own speedup experiments (see, for example, Kambhampati and Chen, 1993, Knoblock, 1993, Minton, 1993] we offer three final caveats. First, as with any statistical test, failure to reject the null hypothesis is inconclusive; it is not a basis for concluding that system s is at least as fast as system f . A more appropriate conclusion is that the experiment should be repeated with a ....

Knoblock, Craig A. 1993. Automatically generating abstractions for planning. To appear in Artificial Intelligence.

....rule that delays the operator application and forces more emphasis on the backward search (Veloso and Stone 1995) we call it DELAY. The distinction between APPLY and DELAY is similar to that between the SAVTA and SABA planners, implemented by Veloso and Stone (1995) The third method, ALPINE (Knoblock 1994), is a combination of APPLY with an abstraction generator, which determines relative importance of elements of a planning domain. ALPINE first ignores the less important elements and builds a solution outline; it then refines the solution, taking care of the initially ignored details. Experiments ....

Knoblock, C. A. 1994. Automatically generating abstractions for planning. Artificial Intelligence 68:243--302.

....in the efficiency of search in various runs of the Monkey and Bananas puzzle. However this paper also develops a computational model which shows that using abstraction may introduce inefficiency. Even worse, in [SP92] Smith and Peot provide a variation of the machine shop example introduced in [Kno94] where an abstraction satisfying the ordered monotonicity property leads to very inefficient reasoning. Their example is constructed as follows. They start by providing a set of operators schemas and order their preconditions in a hierarchy satisfying the ordered monotonicity property. Then they ....

C. A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243--302, 1994.

....without ZLIFO, the number of explored partial plans is reduced from 78606 down to 2209 in the case of the problem with 3 discs. Runtime improves from 65 seconds down to 2 seconds. Similarly, when using bf control without ZLIFO the number of explored partial plans reduces from 1554 down to 873. Knoblock (1994) also reports an improvement in performance for the Prodigy planner (Fink Veloso, 1994) when it is using the abstraction hierarchy generated for this domain by the alpine module, which provides in essence the same information as the goal agenda. 9 6. Summary and Comparison to Related Work Many ....

....of operators and to derive ordering constraints based on the interaction of operators can also be found in a variety of approaches. While we analyze harmful interactions of operators in our method by studying the delete e ects, the approaches described in (Dawsson Siklossy, 1977; Korf, 1985; Knoblock, 1994) concentrate on the positive interactions between operators. The successful matching of e ects to preconditions forms the basis to learn macro operators, see (Dawsson Siklossy, 1977; Korf, 1985) The alpine system (Knoblock, 1994) learns abstraction hierarchies for the Prodigy planner (Fink ....

[Article contains additional citation context not shown here]

Knoblock, C. (1994). Automatically generating abstractions for planning. Articial Intelligence, 68 (2), 243-302.

....is obtained, on the basis of causality and nature of resources. An actual example was shown in Section 4.1. From the abstraction angle, the idea of keeping the structure of the causal plan intact during resource allocation phase is akin to the enforcement of ordered monotonicity property in ALPINE[27]. An important difference however is that our work is not dependent on the availability of strong abstractions, but is rather motivated by the desire to exploit the loose coupling between planning and scheduling in most real world domains. If the abstract plan cannot be scheduled, RealPlan PP ....

Knoblock, C. A. Automatically Generating Abstractions for Planning. AI Journal, 68(2). 1994.

....position. The performance improves signi cantly. Instead of taking 8 s and exploring 2291 partial plans, UCPOP only takes 0.18 0.06 0.01=0.25 s and explores only 48 13 6=67 plans. Unfortunately, any problems or subproblems with more than 3 discs remain beyond the performance of UCPOP. Knoblock [Kno94] also reports an improvement in performance for the Prodigy planner [FV94] when it is using the abstraction hierarchy generated for this domain by the alpine module. 6 Summary and Comparison to Related Work Many related approaches have been developed to provide a planner with the ability to ....

....analyze the e ects and preconditions of operators and to derive ordering 37 constraints based on the interaction of operators can also be found in a variety of approaches. While we analyze harmful interactions of operators in our method by studying the delete e ects, the approaches described in [DS77, Kor85, Kno94] concentrate on the positive interactions between operators. The successful matching of e ects to preconditions forms the basis to learn macro operators in [DS77, Kor85] The alpine system described in [Kno94] learns abstraction hierarchies for the Prodigy planner [FV94] The approach is based on ....

[Article contains additional citation context not shown here]

C. Knoblock. Automatically generating abstraction for planning. Articial Intelligence, 68(2):243-302, 1994.

....the context of making planning efficient, the current work can be seen as the abstraction of resources from planning. From this angle, the idea of keeping the structure of the causal plan intact during resource allocation phase is akin to the enforcement of ordered monotonicity property in ALPINE[22]. An important difference however is that our work is not dependent on the availability of strong abstractions, but is rather motivated by the desire to exploit the loose coupling between planning and scheduling in most real world domains. If the abstract plan cannot be scheduled, the new approach ....

Knoblock, C. A. Automatically Generating Abstractions for Planning. AI Journal, 68(2). 1994.

....state space definition are embeddings. The other main type of abstraction transformation is the homomorphism . Informally, a homomorphism f groups together several states in SS to create a single abstract state. For example, techniques that drop a predicate entirely from a state space description [Knoblock,1994] are homomorphisms. The aim of creating a heuristic is to speed up search. Without a heuristic, A blindly searches in the original space. With a heuristic, A s search will be more focused, and the search effort in the original space will be reduced by some amount (the saving ) The primary ....

Knoblock, C.A. (1994), "Automatically Generating Abstractions for Planning", Artificial Intelligence, vol. 68(2), pp. 243-302.

....and the disadvantage of a highly restricted horizon. Just the opposite holds for long term planning. To adjust the agent s planning horizon properly, we are experimenting with layered planning, which tries to incorporate the advantages of both reactivity and planning (related to abstractions [10, 16] and Hierarchical Task Network (HTN) planning [5, 15] Figure 2 shows the di erent layers of planning, which include coarse grained planning on the intention layer, ne grained planning on the skill layer and execution on the atomic actions layer. Following the principle of decomposed reasoning, ....

Knoblock, C. A.: Automatically generating Abstractions for Planning. Articial Intelligence 68(2). 1994.

No context found.

Knoblock, C. A. (1994a). Automatically generating abstractions for planning. Artificial Intelligence, 68 (2), 243--302.

.... to the agenda data structure (to be considered by establishment refinement later) Goal Selection: The strategy used to select the particular precondition c, s to be established, called the goal selection strategy) can be arbitrary, can depend on some ranking based on precondition abstraction [18,34], and or demand driven (e.g. select a goal only when it is not already necessarily true according to the modal truth criterion [3] The last strategy, called MTC based goal selection, involves reasoning about the truth of a condition in a partially ordered plan, and can be intractable for general ....

C. Knoblock. Automatically Generating Abstractions for Planning. Artificial Intelligence, Vol. 68, 1994.

No context found.

Knoblock, C. A. 1994. Automatically generating abstractions for planning. Artificial Intelligence 68.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

No context found.

Knoblock, C. A. 1994. Automatically generating abstractions for planning. Artificial Intelligence 68(2):243--302.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68, 1994.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68:243--302, 1994.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

No context found.

C. A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243 -- 302, 1994.

No context found.

Knoblock, C. (1994). Automatically generating abstractions for planning. Arti cial Intelligence, 68(2):243 - 302.

No context found.

C Knoblock. Automatically generating abstractions for planning. Articial Intelligence, 68(2):243302, 1994.

No context found.

C. A. Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

No context found.

Craig A. Knoblock. Automatically generating abstractions for planning. Arti cial Intelligence, 68(2):243-302, 1994.

No context found.

Craig Knoblock. Automatically generating abstractions for planning. Artificial Intelligence, 68(2):243--302, 1994.

No context found.

C. A. Knoblock. Automatically Generating Abstractions for Planning. Arti cial Intelligence, Vol. 68, pp. 243-302, 1994.

No context found.

Knoblock, C. (1994). Automatically generating abstractions for planning. Artificial Intelligence, 68, No. 2.

No context found.

Knoblock, C.A. (1994), Automatically Generating Abstractions for Planning, Artificial Intelligence, vol. 68(2), pp. 243-302.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC