Kutluhan Erol, James Hendler, and Dana S. Nau. Complexity results for hierarchical tasknetwork planning. Annals of Mathematics and Artificial Intelligence, 18:69--93, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in [PT87] Methods from [MGA97] were applied in [LGM98a] to show complexity results for planners, as described in the AI literature. The AI planning community has analyzed the complexity of several variations of MDPs and a wide variety of other related models. Most of these AI papers, especially [Bac95, Byl94, Cha87, EHN96, ENS95], consider the complexity of deterministic control processes 1 . The complexity of evaluation and existence problems for these systems is generally lower than for stochastic processes (except [GLM97, Lit96] and one theorem in [Byl94] Many of the complexity results coming out of the AI ....

K. Erol, J. Hendler, and D. Nau. Complexity results for hierarchical tasknetwork planning. Annals of Mathematics and Artificial Intelligence, 1996.

....(cf. Corollary 5.3, compare to PSPACE completeness in [30, Theorem 6] Unobservable MDPs were also considered in [12] Beauquier et al. 6] considered different optimality criteria, and thus their results are not directly comparable with ours. Most of the related AI papers, especially [3, 13, 14, 16, 18], consider computationally simpler problems without probabilistic transitions. Thus, the complexity of their problems is generally lower than of ours (except [20, 24] and one theorem in [13] Many of the results are for succinctly represented systems, described by 2 Phase Temporal Bayes Nets [9, ....

K. Erol, J. Hendler, and D. Nau. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence, 1996.

....and Tsitsiklis [22] considered a different policy existence problem, to which the problem to determine an optimal policy does not polynomial time reduce, whereas it does so in our work. Beauquier et al. 5] considered different optimality criteria. Most of the related AI literature, especially [9, 11, 10] consider computationally simpler problems without probabilistic transitions. Thus, the complexity of their problems is generally lower than of ours (except [18, 14] and one theorem in [9] 1 Introduction Partially observable Markov Decision Processes (POMDPs) are ubiquitous in the world of ....

....policy existence problem for unobservable, succcinct MDPs with nonnegative rewards is PSPACE complete. In Theorem 6.1 we show PSPACE completeness even of the stochastic version of this problem. Unobservable MDPs were also considered in [8] under the aspect of approximability. Other work, such as [11, 10], concentrates on computationally simpler problems than those considered here, primarily because they do not use probabilistic transitions. We give formal definitions for basic POMDPs in Section 2, and proofs of the basic results in Section 3. Succinctly represented POMDPs are defined and analyzed ....

K. Erol, J. Hendler, and D. Nau. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence, 1996.

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Kutluhan Erol, James Hendler, and Dana S. Nau. Complexity results for hierarchical tasknetwork planning. Annals of Mathematics and Artificial Intelligence, 18:69--93, 1996.

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Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence 18:69--93, 1996.

....planning system will backtrack and try other methods. Formal analyses of HTN planning have shown that it is strictly more expressive than planning with STRIPS style operators (Erol et al. 1994b) and have established properties such as soundness and completeness (Erol et al. 1994a) complexity (Erol et al. 1996), and the efficiency of various control strategies (Tsuneto et al. 1996, 1997) A domain independent HTN planner is available at http: www.cs.umd.edu projects plus umcp manual for experimental use, and domain specific HTN planners are being developed for several practical applications (Aarup et ....

Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence 18:69--93, 1996.

....or calls to external programs. 2. SHOP s expressive power makes it possible to encode highly ecient domaindependent planning algorithms into SHOP. For example, in our experiments [NCLMA99,NCLMA00] SHOP solved the problems orders of magnitude faster than Blackbox [KS99] IPP [KNHD97] and UMCP [EHN96] and several times as fast as TLplan [BK00] SHOP s expressive power also makes it ideal as a basis for integrating planning with external information sources, such as the IMPACT framework as described in this paper. 3. IMPACT The IMPACT project (see [ESP99,SBD 00] and ....

K. Erol, J. Hendler, and D. Nau. Complexity Results for Hierarchical TaskNetwork Planning. Annals of Mathematics and Articial Intelligence, 18:69-93, 1996.

....planning. Recent mathematical analyses of HTN planning have shown that it is strictly more expressive than planning with STRIPS style operators (Erol et al. 1994b) and have established a number of properties such as soundness and completeness of planning algorithms (Erol et al. 1994a) complexity (Erol et al. 1996), and the relative efficiency of various control strategies (Tsuneto et al. 1996; Tsuneto et al. 1997) A domain independent HTN planner is available at http: www.cs.umd.edu projects plus umcp manual for use in experimental studies, and domain specific HTN planners are being developed for ....

Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence 18:69--93, 1996.

....optimal cutting parameters; thus IMACS s estimates involve considerable approximation. As shown in Figure 9, these steps correspond to a task decomposition somewhat analogous to that used in HTN planning [ Sacerdoti, 1977; Tate, 1977; Wilkins, 1990; 1988; Yang, 1990; Kambhampati and Hendler, 1992; Erol et al. 1995a; 1994 ] Since each FBM can lead to several different operation plans, IMACS does the above steps inside a depthfirst branch and bound search, evaluating the plans as Table 1: Estimated production time for the operation plan shown in Figure 8. Operation Time (min) Operation Time (min) drill h1 ....

K. Erol, J. Hendler, and D. S. Nau. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence, 1995, to appear.

....difficulty is the differences in how AI planning researchers and manufacturing planning researchers view the world. For example, the first author s work on manufacturing planning (e.g. 27, 21, 22, 28, 15, 16, 14, 13, 12, 3, 31] has significantly influenced his research on AI planning (e.g. [9, 41, 10, 6, 5, 20, 4]) and vice versa. However, this influence is not particularly evident in the publications themselves, because they were written to address two different audiences, who have different ideas of what the important problems are and how they should be solved: ffl AI planning researchers usually want ....

....as [39, 38] As an example, Table 1 shows the estimated production time for the operation plan of Figure 6. 3 Comparison with AI Planning Two of the most popular approaches to AI planning are STRIPS style planning 1 [8, 2, 1, 9, 25, 24, 42, 30, 6] and hierarchical task network (HTN) planning [33, 35, 37, 36, 40, 19, 5, 4]. In both cases, the planner typically starts with some initial state that is represented as a collection of logical atoms. In STRIPS style planning, the objective is to produce a state that satisfies a goal condition expressed as a collection of logical atoms, and the planner produces the plan ....

K. Erol, J. Hendler, and D. Nau. Complexity results for hierarchical task-network planning. Annals of Mathematics and Artificial Intelligence, (CS-TR-3240, UMIACS-TR-94-32), 1994. To appear.

....according to this definition of expressivity. Thus, we can conclude the following: Theorem 5 The htn language is strictly more expressive than the strips language with respect to operational expressivity. The details of the definition of operational expressivity and the proof can be found in (Erol et al. 1994b) Note that in previous definitions of expressivity, is not restricted to be computable in polynomial time (or even to be computable at all ) nor are there any restrictions on the size of ( Gamma) in terms of the size of Gamma. In defining expressivity, one can discard the equivalence of ....

....that can be represented in L 2 such that any planning problem P in L 1 has a solution iff (P) also has a solution. This definition of expressivity for a planning language is based on the computational complexity of telling which planning problems represented in that language have solutions. In (Erol et al. 1994b) we show that the complexity of htn planning is strictly semi decidable, whereas in (Erol et al. 1992a) we show that the complexity of strips style planning is much easier, more specifically, EXPSPACEcomplete. This clearly shows that there does not exist any computable transformation from ....

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Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. To appear in Annals of Mathematics and Artificial Intelligence Also available as Technical report CS-TR-3240, UMIACS-TR-94-32, ISR-TR-9510, Computer Science Dept., University of Maryland, March 1994.

....are used to associate effects to actions (primitive tasks) The fundamental difference between strips style planning and htn planning is the representation of desired change in the world. htn planning replaces strips style goals with tasks and task networks, which are provably more powerful (Erol et al. 1994c; Erol et al. 1994b) There are three types of tasks. Goal tasks, like goals in strips, are properties we wish to make true in the world, such as having a house. Primitive tasks are tasks we can directly achieve by executing the corresponding action, such as moving a block, or turning a switch ....

....effects to actions (primitive tasks) The fundamental difference between strips style planning and htn planning is the representation of desired change in the world. htn planning replaces strips style goals with tasks and task networks, which are provably more powerful (Erol et al. 1994c; Erol et al. 1994b) There are three types of tasks. Goal tasks, like goals in strips, are properties we wish to make true in the world, such as having a house. Primitive tasks are tasks we can directly achieve by executing the corresponding action, such as moving a block, or turning a switch on. Compound tasks ....

[Article contains additional citation context not shown here]

Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. To appear in Annals of Mathematics and Artificial Intelligence Also available as Technical report CS-TR-3240, UMIACS-TR-94-32, Computer Science Dept., University of Maryland, March 1994.

....other aspects. In particular, functions are often provided which can debug partially reduced task networks to eliminate potential problems. These critic functions are used to handle ordering constraints, resource limits, and to provide domain specific guidance. The formalization described in (Erol et al. 1994a) explains critics and the relationship between these and the constraints described above. For the purposes of this paper, the critics do not affect worst case behavior, and thus we will omit this detail. Details Our language L for htn planning is a first order language with some extensions. ....

....which confines the planner to plans of length at most exponential in the length of the input. Operational Semantics In this section, we give a syntactic characterization of the set of solutions for a given htn planning problem. Description of an equivalent model theoretic semantics appear in (Erol et al. 1994a) Let d be a primitive task network (one containing only primitive tasks) and let I be the initial state. A plan oe is a completion of d at I, denoted by oe 2 comp(d; I; D) if oe is a total ordering of the primitive tasks in a ground instance of d that satisfies the constraint formula of d. ....

[Article contains additional citation context not shown here]

Erol, K.; Hendler, J.; and Nau, D. Complexity results for hierarchical task-network planning. To appear in Annals of Mathematics and Artificial Intelligence Also available as Technical report CS-TR-3240, UMIACS-TR-94-32, Computer Science Dept., University of Maryland, March 1994.

....and correctly) without an in depth understanding of the implementation details of the critic mechanisms. To reason about analytical properties of such mechanisms (i.e. systematicity, soundness, completeness) a general model of interactions and critics is clearly needed. The work described in [ Erol et al. 1994a; 1994b ] presents a formal model for HTN planning, which provides a constraint based representation for interactions among tasks and enables principled approaches to conflict detection and handling in HTN planning. This paper presents conflict management and constraint handling techniques based ....

....framework. Among the properties of these techniques are soundness, completeness and systematicity. These techniques have been implemented in UMCP, an HTN planning system. 2 An Overview of HTN planning Here is a brief informal description of HTN planning. For a precise formal description, see [ Erol et al. 1994a; 1994b ] htn planning representations for actions and states of the world are similar to those used in strips style planning. 3 Each state of the world is represented by the set of atoms true in that state. Actions, which in htn planning are usually called primitive tasks, correspond to ....

[Article contains additional citation context not shown here]

Erol, K.; Hendler, J. and Nau, D. Complexity results for hierarchical task-network planning. To appear in Annals of Mathematics and Artificial Intelligence Also available as Technical report CS-TR-3240, UMIACS-TR-94-32, ISR-TR-9510 Computer Science Dept., University of Maryland, March 1994.

....work on the properties of HTN planners. One of the primary obstacles impeding such work has been the lack of a clear theoretical framework explaining what a HTN planning system is. To address this problem, some of us (together with Jim Hendler) are developing a formalization of HTN planning [12,9]. We intend to use this formalism to correctly define, explicate, and analyze various properties of HTN planning systems, such as soundness, completeness, complexity, and expressivity. Acknowledgement We appreciate the useful comments about this paper that we received from Tom Bylander, Jim ....

K. Erol, J. Hendler, and D. Nau. Complexity results for hierarchical task-network planning. 1993. Submitted for journal publication.

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Kutluhan Erol, James A. Hendler, and Dana S. Nau. Complexity results for hierarchical tasknetwork planning. Annals of Mathematics and Artificial Intelligence, 18:69--93, 1996.

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