K. Erol, D.S. Nau, and V.S. Subrahmanian. On the complexity of domain-independent planning. In Proceedings AAAI-92, pages 381--386, San Jose, CA, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the committed steps. Mali and Kambhampati point out that causal encodings provide a solution to this problem. Although causal 8 It seems unlikely that step by step compilation can be avoided. This compilation process is forced by the fact that the general planning problem is PSPACE complete [Erol et al. 1992] . In order to compile to the NP complete problem of constraint satisfaction, a planning problem must be constrained somehow to become an NP complete problem [Kautz et al. 1996] Restricting solution length is the only technique currently used to achieve this reduction and the only one of which ....

K. Erol, D. Nau, and V. Subrahmanian. On the complexity of domain-independent planning. In Proceedings of the Tenth National Conference on Artificial Intelligence, July 1992.

....the world after each action is known in advance, so sensing is unnecessary and planning can be performed in a fully open loop fashion. Even under these conditions planning is hard: in the first order case undecidable, in the propositional case PSPACEcomplete, and in the bounded length NP complete [19, 16, 29, 16]. The combinatorial challenge of classical planning comes from the large size and branching factor of the search space; enumeration of even the states within a fixed distance of the initial state is in general infeasible. The most straightforward planning technique is A backtrack search, forward ....

K. Erol, D. Nau, and V. Subrahmanian. On the complexity of domain-independent planning. In Proceedings of AAAI-92, pages 381--386. AAAI Press, 1992.

.... 1995 and appears in [3] This was done when Fahiem Bacchus was at the 1 context, in which actions are represented using the STRIPS representation and the initial and goal states are specified as lists of literals, even restricted versions of the planning problem are known to be PSPACE complete [20]. Although informative, these worst case hardness results do not mean that computing plans is impossible. As we will demonstrate many domains offer additional structure that can ease the difficult of planning. There are a variety of mechanisms that can be used to exploit structure so as to make ....

K. Erol, D.S. Nau, and V.S. Subrahmanian. On the complexity of domain-independent planning. In Proceedings of the AAAI National Conference, pages 381--386, 1992.

....planning in Artificial Intelligence has for decades concentrated on theoretical issues of planning algorithms. Recent work has concentrated on, for example, the relative performance of total order vs partial order planners [3, 57, 44] the inherent computational complexity of plan generation [6, 23], extending the expressiveness of the classical 1 model [25] and general, theoretical frameworks for planning engines [31] This research has been dominated by the use of the literal or proposition as the basic level of representation, and operators representing actions, as the basic knowledge ....

K. Erol, D. S. Nau, and V. S. Subrahmanian. On the complexity of domain-independent planning. In Tenth National Conference on Artificial Intelligence, 1992.

....Further, we believe that if having a sufficiently deep understanding of the problem structure, it is better to use other methods than heuristics. Some tractability results have been reported in the literature for restrictions on the propositional Strips formalism [ Bylander, 1992a, Bylander, 1994, Erol et al. 1992 ] and for restrictions on the related state variable formalism SAS [ Backstrom and Klein, 1991, Backstrom and Nebel, 1993 ] These results are all based on essentially syntactic restrictions on the set of operators. Syntactic restrictions are very appealing to study, since, typically, they ....

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386.

....seem to have assumed that at least some of these formalism exhibit different expressive power. The discovery that this is, in fact, not the case lead us to pose the question of which features actually do add to the expressiveness of a planning formalism. Complexity analyses have been presented [6, 9, 12] for restricted versions of the formalisms in this report, thus telling us something about the relative expressive power of restricted cases within some of the formalisms. However, even the unrestricted cases considered in this report are often considered too limited for most practical ....

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In Proceedings of the 10th (US) National Conference on Artificial Intelligence (AAAI-92), pages 381-- 386, San Jos'e, CA, USA, July 1992. American Association for Artificial Intelligence.

....easily be achieved by storing each H[i] separately, using negligible O(H) preprocessing time. 34 6 Discussion and Conclusions Recently a number of results have been published on the computational complexity of propositional STRIPS planning under various restrictions [ Bylander, 1991, 1992a, Erol et al. 1992 ] In addition to these we have previously presented a number of tractable planning problems using the SAS formalism [ Backstrom and Klein, 1991a, 1991b, Backstrom, 1992a, 1992b ] All of these results concern the complexity of planning in various restricted versions of certain formalisms. ....

....complexity for each of the possible combinations of the previously considered restrictions. We already know [ Backstrom, 1992a, 1992b ] that the SAS formalism is expressively equivalent to a number of standard propositional STRIPS formalisms, including those analyzed by Bylander [ 1991 ] and Erol et al. 1992 ] One might wonder, then, why we have bothered doing such a complexity analysis for the SAS formalism since the equivalence implies that the previously known complexity results carry over. There are, however, at least two important differences between our analysis and the previous ones. ....

[Article contains additional citation context not shown here]

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386.

....Further, we believe that if having such a deep understanding of the problem structure, it is better to use other methods than heuristics. Some tractability results for planning has been reported in the literature lately [ Backstrom and Klein, 1991, Backstrom and Nebel, 1993, Bylander, 1994, Erol et al. 1992 ] However, apart from being very restricted, they are all based on essentially syntactic restrictions on the set of operators. Syntactic restrictions are very appealing to study, since they are typically easy to define and not very costly to test. However, to gain any deeper insight into what ....

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386. 38

....case. Even worse, there exists propositional planning problems with exponentially sized minimal solutions [ Backstrom and Klein, 1991b ] thus making the generation problem for propositional planning provably intractable. A number of restricted cases have been analysed by Bylander [ 1994 ] and Erol et al. [ 1992 ] and their complexity range from Pspace complete to, in rare cases, tractable. These restricted cases are based on simple syntactic restrictions on operators, such as bounding the number of pre and post conditions. Using multi valued state variables instead of propositional atoms cannot, of ....

....planning. The first result concerning the complexity of first order planning was presented by Chapman [ 1987 ] who showed that first order planning is undecidable. The proof made use of a planning problem with an infinite number of variables, which is hardly a realistic assumption. However, Erol et. al [ 1992 ] cleaned up this result by proving (with a less contrived proof) that first order planning is undecidable if there are function symbols or infinitely many constants in the language. If no function symbols and only finite domains are allowed, first order planning is decidable with a complexity ....

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386.

....Restrictions Until recently, we worked only with the syntactical restrictions in the previous section. Similarly, other results in the literature on planning complexity also considered syntactical restrictions only, e.g. restricting the number and or polarity of atoms in the precondition [18, 25]. Syntactical restrictions are very appealing to study since, typically, they are easy to define and not very costly to test. However, to gain any deeper insight into what makes planning problems hard and easy respectively probably require that we study the structure of the problem, in particular ....

K. Erol, D. S. Nau, and V. S. Subrahmanian. On the complexity of domainindependent planning. In Proc. 10th (US) Nat'l Conf. on Artif Intell. (AAAI92) , pages 381--386, San Jos'e, CA, USA, 1992.

....observations have motivated research into identifying restrictions that make hard problems tractable in other areas than planning, e.g. concept languages [65, 75] and abduction [70] Tractable planning problems have been identified, especially by ourselves (see Section 4.2. 1) but also by others [66, 67, 76]. 4.1.3 Applications in Automatic Control Although of general, theoretical nature, our research has to a large extent been motivated by the application area of sequential control within the subarea discrete event dynamic systems of automatic control where many problems can be viewed as planning ....

....have motivated us to follow the restricted problems line of research, trying to identify tractable planning problems. In 1990 we presented the, to our knowledge, first ever tractable planning problem, the SAS PUBS problem [59, 61] In contrast to other, more recent publications into this topic [66, 76] we did not use the formalism per se as a guide to which restrictions to use. Instead we identified inherent restrictions in a toy problem in the sequential control domain, the tunnel problem [51] These restrictions, denoted P, U, B and S, are essentially syntactic restrictions on the sets of ....

[Article contains additional citation context not shown here]

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [44], pages 381--386.

....the work on planning and our knowledge compilation framework is that the former concentrates on solving single problem instances, rather than shifting computational effort from on line to offline. All but the most restricted forms of planning are NP hard [Gupta and Nau, 1991; Bylander, 1991; Erol et al. 1992] Therefore, the best known planning algorithms run in exponential time. Work on planning with abstraction attempts to lower the exponent. By contrast, the aim in the knowledge compilation framework is to pre process (compile) a theory in such a manner that queries (problem instances) can be ....

Erol, K.; Nau, D.S.; and Subrahmanian, V.S. 1992. On the complexity of domain-independent planning. In Proceedings AAAI-92, 381--386.

....of other planners as well. The effectiveness of the system hinges mainly on the learning strategy and on extraction of the relevant features. Keywords: case based planning, learning, feature extraction 1 Introduction Domain independent planning has been shown to be intractable and undecidable [2,3,4]. Thus, saving and adapting previously constructed plans in order to improve the average case efficiency of planning by avoiding repetition of planning effort is largely regarded as a promising approach. Earliest research on planning from experience is the motion planning of the robot named Shakey ....

K. Erol, D.S. Nau and V.S. Subrahmanian, On the complexity of domain-independent planning, in: Proceedings AAAI-92, San Jose, CA (MIT Press, Cambridge, MA, 1992) 381-386.

....structures 1. INTRODUCTION Planning is the reasoning problem of finding a (totally or partially ordered) set of operators that achieves a specified goal from a given initial state. 1 It is well known that this problem is computationally intractable 2 in general (Chapman 1987; Bylander 1994; Erol et al. 1992). In fact, domain independent planning systems that are guaranteed to find a solution if there exists one, i.e. complete planners, are bogged down by the huge search space. 3 One way to deal with this problem is to use heuristic search techniques and to sacrifice completeness. Another way is to ....

....is a very severe restriction that simplifies the planning process considerably because for each value of a state variable there is at most one operator that can achieve this value. Single valuedness resembles the restriction that only positive preconditions are allowed (Bylander 1991; Erol et al. 1992), but is slightly more general in that single valuedness only applies to the preconditions such that the corresponding state variables are not changed. The two latter restrictions are local to the operators. Binariness is just the restriction we find in propositional STRIPS and ground TWEAK, ....

[Article contains additional citation context not shown here]

Erol, K., Nau, D. S., and Subrahmanian, V. S. 1992. On the complexity of domain-independent planning. In AAAI-92 (1992), pages 381--386.

....Many structural constraints have been identified that a learning system could exploit for more effective inference. For example, general purpose problem solvers provide flexible representations that can encode a variety of domains of discourse, but these cannot be reasoned with tractably [Bylander92, Chapman87, Eorl92, Freuder82]. However, this full generality is often unnecessary given the structure of a particular application. In contrast, there are a variety of effective problem solving techniques that apply if a domain obeys certain structural restrictions. For example, Eorl, Nau and Subrahmanian summarize complexity ....

....there are a variety of effective problem solving techniques that apply if a domain obeys certain structural restrictions. For example, Eorl, Nau and Subrahmanian summarize complexity results for several specializations of STRIPS operators, some of which support worst case polynomial planning [Eorl92]. Constraint satisfaction problems can be solved efficiently if the constraint graph is expressible as a tree [Dechter87, Freuder82] Korfshowsadomainsupportsefficientproblemsolving if it exhibits thepropertyof serial decomposability [Korf87] Many integer programming programming problems can be ....

K. Eorl, D. S. Nau and V. S. Subrahmanian, "On the Complexity of Domain--Independent Planning," Proceedings of the National Conference on Artificial Intelligence, San Jose, CA, July 1992, pp. 381--386.

....Planning is the reasoning problem of finding a (totally or partially ordered) set of operators that achieves a specified goal from a given initial state. 1 It is well known that this problem is computationally intractable 2 in general [ Chapman, 1987; Bylander, 1991; Bylander, 1994; Erol et al. 1992 ] In fact, domainindependent planning systems that are guaranteed to find a solution if there exists one, i.e. complete planners, are bogged down by the huge search space. 3 One way to deal with this problem is to use heuristic search techniques and to sacrifice completeness. Another way is ....

....Action Structures, denoting that the formalism is a restriction of the action structure formalism [Sandewall and Ronnquist, 1986] at most one operator that can achieve this value. Single valuedness resembles the restriction that only positive preconditions are allowed [ Bylander, 1991; Erol et al. 1992 ] but is slightly more general in that single valuedness only applies to the preconditions such that the corresponding state variables are not changed. The two latter restrictions are local to the operators. Binariness is just the restriction we find in propositional STRIPS and ground TWEAK, ....

[Article contains additional citation context not shown here]

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386.

....seem to have assumed that at least some of these formalism exhibit different expressive power. The discovery that this is, in fact, not the case lead us to pose the question of which features actually do add to the expressiveness of a planning formalism. Complexity analyses have been presented [6,9,12] for restricted versions of the formalisms in this article, thus telling us something about the relative expressive power of restricted cases within some of the formalisms. However, even the unrestricted cases considered in this article are often considered too limited for most practical ....

K. Erol, D. S. Nau, and V. S. Subrahmanian. On the complexity of domainindependent planning. In Proceedings of the 10th (US) National Conference on Artificial Intelligence (AAAI-92), pages 381--386, San Jos'e, CA, USA, July 1992. American Association for Artificial Intelligence.

....and output it in a predetermined orientation (Natarajan, 1986) may also be viewed as a special case of our framework. Our work is concerned with the off line and on line tractability of Planning while Learning. This relates it to work concerned with the tractability of different types of planning (Erol, Nau, Subrahmanian, 1992; Bylander, 1992) This work mainly concentrated on on line tractability of a single agent planning with complete information. Our work concentrates on general computational aspects of planning with incomplete information, considers also multi agent situations, and discusses both on line and ....

Erol, K., Nau, D., & Subrahmanian, V. (1992). On the Complexity of Domain-Independent Planning. In Proceedings of AAAI-92, pp. 381--386.

....in the computational aspects of planning during recent years. It is now well known that planning is computationally hard in the general case. The first result concerning the complexity of first order planning was presented by Chapman [ 1987 ] who showed that first order planning is undecidable. Erol et. al [ 1992 ] strengthened this result by proving (with a less contrived proof) that first order planning is undecidable if there are function symbols or infinitely many constants in the language. If no function symbols and only finite domains are allowed, first order planning is decidable with a complexity ....

....1994 ] Even worse, there exist propositional planning problems with exponentially sized minimal solutions [ Backstrom and Klein, 1991b ] thus making the generation problem for propositional planning provably intractable. A number of restricted cases have been analysed by Bylander [ 1994 ] and Erol et al. [ 1992 ] and their complexity ranges from Pspace complete to, in rare cases, tractable. These restricted cases are based on simple syntactic restrictions on operators, such as bounding the number of pre and post conditions. Using multi valued state variables instead of propositional atoms cannot, of ....

Kutluhan Erol, Dana S Nau, and V S Subrahmanian. On the complexity of domain-independent planning. In AAAI-92 [ 1992 ] , pages 381--386.

....stationary environments, we see the study of Planning while Executing in non stationary environments as a promising direction for future research. Section 6 can be considered as a first step in this direction. Our work is also related to work on the tractability of different types of planning [ENS92, Byl92] However, these works concentrate on planning with complete information. Our work is complementary to previous work on the complexity of conditional planning [ST94] The latter work discusses the generation of conditional plans as an approach to planning with incomplete information, while ....

K. Erol, D.S. Nau, and V.S. Subrahmanian. On the Complexity of Domain-Independent Planning. In Proc. of AAAI-92, pages 381--386, 1992.

....[3] has argued that there are various inadequacies in the Gelfond Lifschitz framework. He has suggested a new language that incorporates actions into logic programming, studied the semantics of this language, and proven various elegant soundness and completeness results. Erol, Nau and Subrahmanian[4] have shown that there is a very simple and natural translation of planning domains (whose operations have empty delete lists) to negation free logic programs such that a goal G can be achieved from the planning domain iff a related goal can be proved from the negation free logic program obtained ....

K. Erol, D.S. Nau and V.S. Subrahmanian. (1992) On the Complexity of Domain-Independent Planning, Proc. AAAI-92, MIT Press, July 1992.

No context found.

K. Erol, D.S. Nau, and V.S. Subrahmanian. On the complexity of domain-independent planning. In Proceedings AAAI-92, pages 381--386, San Jose, CA, 1992.

No context found.

K. Erol, D.S. Nau, and V.S. Subrahmanian. On the complexity of domain-independent planning. In Proceedings of the AAAI National Conference, pages 381--386, 1992.

No context found.

K. Erol, D. S. Nau, and V. S. Subrahmanian, On the complexity of domain-independent planning, in: Proc. AAAI'92 (AAAI Press/MIT Press, 1992) 381--386.

No context found.

K. Erol, D. Nau, and V.S. Subrahmanian. On the complexity of domain-independent planning. In AAAI 92, pages 381--386, 92. R. Firby. An investigation into reactive planning in complex domains. In AAAI 87, 1987.

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