Abstract
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).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 241-267 |
| Number of pages | 27 |
| Journal | Artificial Intelligence |
| Volume | 122 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 2000 |
Fingerprint
ASJC Scopus subject areas
- Artificial Intelligence
- Computational Theory and Mathematics
Cite this
Computational complexity of planning and approximate planning in the presence of incompleteness. / Baral, Chitta; Kreinovich, Vladik; Trejo, Raúl.
In: Artificial Intelligence, Vol. 122, No. 1, 09.2000, p. 241-267.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Computational complexity of planning and approximate planning in the presence of incompleteness
AU - Baral, Chitta
AU - Kreinovich, Vladik
AU - Trejo, Raúl
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).
UR - http://www.scopus.com/inward/record.url?scp=0034271027&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034271027&partnerID=8YFLogxK
U2 - 10.1016/S0004-3702(00)00043-6
DO - 10.1016/S0004-3702(00)00043-6
M3 - Article
VL - 122
SP - 241
EP - 267
JO - Artificial Intelligence
JF - Artificial Intelligence
SN - 0004-3702
IS - 1
ER -