TY - JOUR
T1 - Computational complexity of planning and approximate planning in the presence of incompleteness
AU - Baral, Chitta
AU - Kreinovich, Vladik
AU - Trejo, Raúl
N1 - Funding Information:
This work was supported in part by NASA under cooperative agreements NCC5-97 and NCC5-209, by NSF grants No. DUE-9750858 and IRI-9501577, by United Space Alliance, grant No. NAS 9-20000 (PWO C0C67713A6), by Future Aerospace Science and Technology Program (FAST) Center for Structural Integrity of Aerospace Systems, effort sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number F49620-95-1-0518, and by the National Security Agency under Grants No. MDA904-98-1-0564 and MDA904-98-1-0561.
PY - 2000/9
Y1 - 2000/9
N2 - In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there have been proposals to use `sensing' actions to plan in the presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1991 by Gelfond and Lifschitz, and its extensions. It is known that if we consider only plans of tractable (polynomial) duration, planning in A - with complete information about the initial situation - is NP-complete: even checking whether a given objective is attainable from a given initial state is NP-complete. In this paper, we show that the planning problem in the presence of incompleteness is indeed harder: it belongs to the next level of the complexity hierarchy (in precise terms, it is Σ2P-complete). To overcome the complexity of this problem, Baral and Son have proposed several approximations. We show that under certain conditions, one of these approximations - 0-approximation - makes the problem NP-complete (thus indeed reducing its complexity).
AB - In the last several years, there have been several studies about the computational complexity of classical planning assuming that the planner has complete knowledge about the initial situation. Recently, there have been proposals to use `sensing' actions to plan in the presence of incompleteness. In this paper we study the complexity of planning in such cases. In our study we use the action description language A proposed in 1991 by Gelfond and Lifschitz, and its extensions. It is known that if we consider only plans of tractable (polynomial) duration, planning in A - with complete information about the initial situation - is NP-complete: even checking whether a given objective is attainable from a given initial state is NP-complete. In this paper, we show that the planning problem in the presence of incompleteness is indeed harder: it belongs to the next level of the complexity hierarchy (in precise terms, it is Σ2P-complete). To overcome the complexity of this problem, Baral and Son have proposed several approximations. We show that under certain conditions, one of these approximations - 0-approximation - makes the problem NP-complete (thus indeed reducing its complexity).
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U2 - 10.1016/S0004-3702(00)00043-6
DO - 10.1016/S0004-3702(00)00043-6
M3 - Article
AN - SCOPUS:0034271027
VL - 122
SP - 241
EP - 267
JO - Artificial Intelligence
JF - Artificial Intelligence
SN - 0004-3702
IS - 1
ER -