메뉴 건너뛰기




Volumn 47, Issue 4, 2000, Pages 681-720

Complexity of finite-horizon Markov decision process problems

Author keywords

Computational complexity; Markov decision processes; NP; NPPP; Partially observable Markov decision processes; PL; PSPACE; Succinct representations

Indexed keywords

CONTROLLED STOCHASTIC SYSTEMS; MARKOV DECISION PROCESSES; PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES (POMPD);

EID: 0001205548     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/347476.347480     Document Type: Article
Times cited : (155)

References (92)
  • 1
    • 0030554482 scopus 로고    scopus 로고
    • Relationships among PL, #L, and the determinant. ^ KAIRO Theoret
    • ALLENDER, E., AND OGIHARA, M. 1996. Relationships among PL, #L, and the determinant. ^ KAIRO Theoret. Inf. Appl. 30, 1, 1-21.
    • (1996) Inf. Appl. , vol.30 , pp. 1-21
    • Allender, E.1    Ogihara, M.2
  • 2
    • 38049091720 scopus 로고
    • A very hard log-space counting class
    • ALVAREZ, C., AND JENNER, B. 1993. A very hard log-space counting class. Theoret. Compiit. Sei. 107, 3-30.
    • (1993) Theoret. Compiit. Sei. , vol.107 , pp. 3-30
    • Alvarez, C.1    Jenner, B.2
  • 3
    • 0037919794 scopus 로고
    • Optimal control of partially observed Markovian systems
    • AOKI, M. 1965. Optimal control of partially observed Markovian systems. J. Franklin Inst. 280, 367-368.
    • (1965) J. Franklin Inst. , vol.280 , pp. 367-368
    • Aoki, M.1
  • 4
    • 0010362432 scopus 로고    scopus 로고
    • A temporal Bayesian network for diagnosis and prediction
    • ARROYO-FIGUEROA, G., AND SUGAR, L. E. 1999. A temporal Bayesian network for diagnosis and prediction. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. MorganKaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Arroyo-Figueroa, G.1    Sugar, L.E.2
  • 5
    • 50549213583 scopus 로고
    • Optimal control of Markov processes with incomplete state information
    • ASTROM, K. 1965. Optimal control of Markov processes with incomplete state information. J. Math. Andy. Appl 10, 174-205.
    • (1965) J. Math. Andy. Appl , vol.10 , pp. 174-205
    • Astrom, K.1
  • 6
    • 0029332894 scopus 로고
    • Expressive equivalence of planning formalisms
    • BÄCKSTROM, C. 1995. Expressive equivalence of planning formalisms. Artif. Int. 76, 17-34.
    • (1995) Artif. Int. , vol.76 , pp. 17-34
    • Bäckstrom, C.1
  • 8
    • 81055135894 scopus 로고    scopus 로고
    • An application of uncertain reasoning to requirements engineering
    • BARRY, P., AND LASKEY, K. B. 1999. An application of uncertain reasoning to requirements engineering. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. MorganKaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Barry, P.1    Laskey, K.B.2
  • 13
    • 0032666946 scopus 로고    scopus 로고
    • Decision-theoretic planning
    • BLYTHE, J. 1999. Decision-theoretic planning. AI Magazine 20, 2, 37-54.
    • (1999) AI Magazine , vol.20 , pp. 37-54
    • Blythe, J.1
  • 14
    • 16344372011 scopus 로고    scopus 로고
    • Artificial decision making in intelligent buildings
    • BOMAN, DAVIDSSON, AND YOUNES. 1999. Artificial decision making in intelligent buildings. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Boman1    Davidsson2
  • 15
    • 0013580273 scopus 로고
    • Planning under uncertainty: Structural assumptions and computational leverage
    • BOUTILIER, C., DEAN, T., AND HANKS, S. 1995a. Planning under uncertainty: Structural assumptions and computational leverage. In Proceedings of the 2nd European Workshop on Planning.
    • (1995) In Proceedings of the , vol.2
    • Boutilier, C.1    Dean, T.2    Hanks, S.3
  • 16
    • 0346942368 scopus 로고    scopus 로고
    • Decision-theoretic planning: Structural assumptions and computational leverage
    • BOUTILIER, C., DEAN, T., AND HANKS, S. 1999a. Decision-theoretic planning: Structural assumptions and computational leverage. J. AI Res. 11, 1-94.
    • (1999) J. AI Res. , vol.11 , pp. 1-94
    • Boutilier, C.1    Dean, T.2    Hanks, S.3
  • 18
    • 1142292878 scopus 로고    scopus 로고
    • Continuous value function approximation for sequential bidding policies
    • BOUTILIER, C., GOLDSZMIDT, M., AND SABATA, B. 1999b. Continuous value function approximation for sequential bidding policies. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Boutilier, C.1    Goldszmidt, M.2    Sabata, B.3
  • 19
    • 0026107125 scopus 로고
    • On the complexity of VLSI implementations and graph representations of boolean functions with application to integer multiplication
    • BRYANT, R. E. 1991. On the complexity of VLSI implementations and graph representations of boolean functions with application to integer multiplication. IEEE Trans. Comput. C-40, 2, 205-213.
    • (1991) IEEE Trans. Comput. C , vol.40 , pp. 205-213
    • Bryant, R.E.1
  • 20
    • 0030570119 scopus 로고    scopus 로고
    • On the complexity of partially observed Markov decision processes
    • BURAGO, D., DE ROUGEMONT, M., AND SLISSENKO, A. 1996. On the complexity of partially observed Markov decision processes. Theoret. Comput. Sei. 157, 2, 161-183.
    • (1996) Theoret. Comput. Sei. , vol.157 , pp. 161-183
    • Burago, D.1    De Rougemont, M.2    Slissenko, A.3
  • 21
    • 0028498153 scopus 로고
    • The computational complexity of propositional STRIPS planning
    • BYLANDER, T. 1994. The computational complexity of propositional STRIPS planning. Artif. Int. 69, 165-204.
    • (1994) Artif. Int. , vol.69 , pp. 165-204
    • Bylander, T.1
  • 22
    • 0003989210 scopus 로고    scopus 로고
    • Exact and Approximate Algorithms for Partially Observable Markov Decision Processes
    • CASSANDRA, A. 1998. Exact and Approximate Algorithms for Partially Observable Markov Decision Processes. Ph.D. dissertation. Brown Univ., Providence, R.I.
    • (1998) Ph.D. Dissertation. Brown Univ., Providence, R.I.
    • Cassandra, A.1
  • 24
    • 0003596835 scopus 로고
    • Efficient dynamic-programming updates in partially observable Markov decision processes
    • Brown Univ., Providence, R.I.
    • CASSANDRA, A., KAELBLING, L., AND LITTMAN, M. 1995. Efficient dynamic-programming updates in partially observable Markov decision processes. Tech. Rep. CS-95-19. Brown Univ., Providence, R.I.
    • (1995) Tech. Rep. CS-95-19.
    • Cassandra, A.1    Kaelbling, L.2    Littman, M.3
  • 25
    • 0001909869 scopus 로고    scopus 로고
    • Incremental pruning: A simple, fast, exact method for partially observable Markov decision processes
    • CASSANDRA, A., LITTMAN, M., AND ZHANG, N. 1997. Incremental pruning: A simple, fast, exact method for partially observable Markov decision processes. In Proceedings of the 13th Conference on Uncertainty in Artificial Intelligence (UAI-97). D. Geiger and P. P. Shenoy, Eds. MorganKaufmann, San Francisco, Calif., pp. 54-61.
    • (1997) In Proceedings of the , vol.13 , pp. 54-61
    • Cassandra, A.1    Littman, M.2    Zhang, N.3
  • 26
    • 0023381915 scopus 로고
    • Planning for conjunctive goals
    • CHAPMAN, D. 1987. Planning for conjunctive goals. Artif. Int. 32, 333-379.
    • (1987) Artif. Int. , vol.32 , pp. 333-379
    • Chapman, D.1
  • 27
    • 0344510322 scopus 로고
    • Controlled random sequences
    • DYNKIN, E. 1965. Controlled random sequences. Theory Prob. Appl. X, 10, 1-14.
    • (1965) Theory Prob. Appl. X , vol.10 , pp. 1-14
    • Dynkin, E.1
  • 28
    • 26444572401 scopus 로고    scopus 로고
    • Complexity results for hierarchical task-network planning
    • EROL, K., HENDLER, J., AND NAU, D. 1996. Complexity results for hierarchical task-network planning. Ann. Math. Artif. Int. 18, 69-93.
    • (1996) Ann. Math. Artif. Int. , vol.18 , pp. 69-93
    • Erol, K.1    Hendler, J.2    Nau, D.3
  • 29
    • 0029332411 scopus 로고
    • Complexity, decidability and undecidability results for domain-independent planning
    • EROL, K., NAU, D., AND SUBRAHMANIAN, V. 1995. Complexity, decidability and undecidability results for domain-independent planning. Artif. Int. 76, 75-88.
    • (1995) Artif. Int. , vol.76 , pp. 75-88
    • Erol, K.1    Nau, D.2    Subrahmanian, V.3
  • 31
    • 0020716037 scopus 로고
    • Succinct representation of graphs
    • GALPERIN, H., AND WIGDERSON, A. 1983. Succinct representation of graphs. Inf. Cont. 56, 183-198.
    • (1983) Inf. Cont. , vol.56 , pp. 183-198
    • Galperin, H.1    Wigderson, A.2
  • 32
    • 0002539999 scopus 로고
    • A statewide pavement management system
    • GOLABI, K., KuLKARNi, R., AND WAY, G. 1982. A statewide pavement management system. Interfaces 12, 5-21.
    • (1982) Interfaces , vol.12 , pp. 5-21
    • Golabi, K.1    Kulkarni, R.2    Way, G.3
  • 33
    • 0442309713 scopus 로고    scopus 로고
    • The complexity of plan existence and evaluation in probabilistic domains
    • GOLDSMITH, J., LITTMAN, M., AND MUNDHENK, M. 1997. The complexity of plan existence and evaluation in probabilistic domains. In Proceedings of the 13th Conference on Uncertainty in AI. Morgan-Kaufmann, San Francisco, Calif.
    • (1997) In Proceedings of the , vol.13
    • Goldsmith, J.1    Littman, M.2    Mundhenk, M.3
  • 38
    • 33749229627 scopus 로고    scopus 로고
    • Approximation Algorithms for NP-Hard Problems
    • HOCHBAUM, D. 1997. Approximation Algorithms for NP-Hard Problems. PWS Publishing Company.
    • (1997) PWS Publishing Company.
    • Hochbaum, D.1
  • 39
    • 0002956570 scopus 로고    scopus 로고
    • SPUDD: Stochastic planning using decision diagrams
    • HOEY, J., ST.-AUBIN, R., Hu, A., AND BOUTILIER, C. 1999. SPUDD: Stochastic planning using decision diagrams. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif., pp. 279-288.
    • (1999) In Proceedings of the , vol.15 , pp. 279-288
    • Hoey, J.1    St-Aubin, R.2    Hu, A.3    Boutilier, C.4
  • 40
    • 0002561422 scopus 로고    scopus 로고
    • Attention-sensitive alerting in computing systems
    • HORVITZ, E., JACOBS, A., AND HOVEL, D. 1999. Attention-sensitive alerting in computing systems. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Horvitz, E.1    Jacobs, A.2    Hovel, D.3
  • 42
    • 0040580852 scopus 로고
    • On probabilistic tape complexity and fast circuits for matrix inversion problems
    • JUNG, H. 1984. On probabilistic tape complexity and fast circuits for matrix inversion problems. In Proceedings of the llth ICALP. Lecture Notes in Computer Science, vol. 172. Springer-Verlag, New York, pp. 281-291.
    • (1984) In Proceedings of the Llth ICALP. Lecture Notes in Computer Science , vol.172 , pp. 281-291
    • Jung, H.1
  • 43
    • 85034593538 scopus 로고
    • On probabilistic time and space
    • JUNO, H. 1985. On probabilistic time and space. In Proceedings of the 12th ICALP. Lecture Notes in Computer Science, vol. 194. Springer-Verlag, New York, pp. 281-291.
    • (1985) In Proceedings of the , vol.12 , pp. 194
    • Juno, H.1
  • 44
    • 33749227809 scopus 로고    scopus 로고
    • Bayesian poker
    • KORB, K. B., NICHOLSON, A. E., AND JITNAH, N. 1999. Bayesian poker. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Korb, K.B.1    Nicholson, A.E.2    Jitnah, N.3
  • 45
    • 0029333536 scopus 로고
    • An algorithm for probabilistic planning
    • KUSHMERICK, N., HANKS, S., AND WELD, D. 1995. An algorithm for probabilistic planning. Artif. Int. 76, 239-286.
    • (1995) Artif. Int. , vol.76 , pp. 239-286
    • Kushmerick, N.1    Hanks, S.2    Weld, D.3
  • 46
    • 0024910920 scopus 로고
    • Polynomial space counting problems
    • LADNER, R. 1989. Polynomial space counting problems. SIAM J. Comput. 18, 1087-1097.
    • (1989) SIAM J. Comput. , vol.18 , pp. 1087-1097
    • Ladner, R.1
  • 49
    • 0031369472 scopus 로고    scopus 로고
    • Probabilistic prepositional planning: Representations and complexity
    • LITTMAN, M. 1997a. Probabilistic prepositional planning: Representations and complexity. In Proceedings of the 14th National Conference on Artificial Intelligence. AAAI Press/The MIT Press, Cambridge, Mass.
    • (1997) In Proceedings of the , vol.14
    • Littman, M.1
  • 50
    • 0031369472 scopus 로고    scopus 로고
    • Probabilistic propositional planning
    • LITTMAN, M. 1997b. Probabilistic propositional planning:. Representations and complexity. In Proceedings of the 14th National Conference on Artificial Intelligence. AAAI Press/MIT Press, Cambridge, Mass.
    • (1997) Representations and Complexity. in Proceedings of the , vol.14
    • Littman, M.1
  • 51
    • 85031930404 scopus 로고    scopus 로고
    • Initial experiments in probabilistic satisfiability
    • LITTMAN, M. L. 1999a. Initial experiments in probabilistic satisfiability. In Proceedings ofAAAI-99. In preparation for conference submission.
    • (1999) In Proceedings OfAAAI , vol.99
    • Littman, M.L.1
  • 52
    • 0032596408 scopus 로고    scopus 로고
    • Initial experiments in stochastic satisfiability
    • LITTMAN, M. L. 1999b. Initial experiments in stochastic satisfiability. In Proceedings of the 16th National Conference on Artificial Intelligence. AAAI Press/MIT Press, Cambridge, Mass.
    • (1999) In Proceedings of the , vol.16
    • Littman, M.L.1
  • 54
    • 11544375673 scopus 로고    scopus 로고
    • The computational complexity of probabilistic plan existence and evaluation
    • LITTMAN, M., GOLDSMITH, J., AND MUNDHENK, M. 1998. The computational complexity of probabilistic plan existence and evaluation. J. AI Res. 9, 1-36.
    • (1998) J. AI Res. , vol.9 , pp. 1-36
    • Littman, M.1    Goldsmith, J.2    Mundhenk, M.3
  • 55
    • 0002679852 scopus 로고
    • A survey of algorithmic methods for partially observed Markov decision processes
    • LOVEJOY, W. 1991. A survey of algorithmic methods for partially observed Markov decision processes. Ann. Oper. Res. 28, 47-66.
    • (1991) Ann. Oper. Res. , vol.28 , pp. 47-66
    • Lovejoy, W.1
  • 56
    • 33749226463 scopus 로고    scopus 로고
    • My brain is full: When more memory helps
    • LUSENA, C, Li, T., SITTINGER, S., WELLS, C., AND GOLDSMITH, J. 1999. My brain is full: When more memory helps. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. pp. 374-381.
    • (1999) In Proceedings of the , vol.15 , pp. 374-381
    • Sittinger, S.1    Wells, C.2    Goldsmith, J.3
  • 57
    • 0032596468 scopus 로고    scopus 로고
    • On the undecidability of probabilistic planning and infinite-horizon partially observable Markov decision problems
    • MADANI, O., HANKS, S., AND CONDON, A. 1999. On the undecidability of probabilistic planning and infinite-horizon partially observable Markov decision problems. In Proceedings of the 16th National Conference on Artificial Intelligence.
    • (1999) In Proceedings of the , vol.16
    • Madani, O.1    Hanks, S.2    Condon, A.3
  • 59
    • 0031624860 scopus 로고    scopus 로고
    • Using caching to solve larger probabilistic planning problems
    • MAJERCIK, S. M., AND LITTMAN, M. L. 1998b. Using caching to solve larger probabilistic planning problems. In Proceedings of 15th National Conference on Artificial Intelligence, pp. 954-959.
    • (1998) In Proceedings of , vol.15 , pp. 954-959
    • Majercik, S.M.1    Littman, M.L.2
  • 60
    • 0002500946 scopus 로고    scopus 로고
    • Solving POMDPs by searching the space of finite policies
    • MEULEAU, N., KIM, K.-E., KAELBLING, L. P., AND CASSANDRA, A. R. 1999. Solving POMDPs by searching the space of finite policies. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence, pp. 417-426.
    • (1999) In Proceedings of the , vol.15 , pp. 417-426
    • Meuleau, N.1    Kim, K.-E.2    Kaelbling, L.P.3    Cassandra, A.R.4
  • 61
    • 33646430192 scopus 로고    scopus 로고
    • Learning finite-state controllers for partially observable environments
    • MEULEAU, N., PESHKIN, L., KIM, K.-E., AND KAELBLING, L. P. 1999. Learning finite-state controllers for partially observable environments. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence, pp. 427-436.
    • (1999) In Proceedings of the , vol.15 , pp. 427-436
    • Meuleau, N.1    Peshkin, L.2    Kim, K.-E.3    Kaelbling, L.P.4
  • 62
    • 0013354585 scopus 로고    scopus 로고
    • Bayes nets in educational assessment: Where the numbers come from
    • MISLEVY, R. J., ALMOND, R. G., YAN, D., AND STEINBERG, L. S. 1999. Bayes nets in educational assessment: Where the numbers come from. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Mislevy, R.J.1    Almond, R.G.2    Yan, D.3    Steinberg, L.S.4
  • 63
    • 0019909899 scopus 로고
    • A survey of partially observable Markov decision processes: Theory, models, and algorithms
    • MONAIIAN, G. 1982. A survey of partially observable Markov decision processes: Theory, models, and algorithms. Manag. Sei. 28, 1-16.
    • (1982) Manag. Sei. , vol.28 , pp. 1-16
    • Monaiian, G.1
  • 64
    • 0034138406 scopus 로고    scopus 로고
    • The complexity of optimal small policies
    • MUNDHENK, M. 2000. The complexity of optimal small policies. Math. Oper. Res. 25, 1, 118-129.
    • (2000) Math. Oper. Res. , vol.25 , pp. 118-129
    • Mundhenk, M.1
  • 65
    • 84947768393 scopus 로고    scopus 로고
    • The complexity of the policy existence problem for partially-observable finite-horizon Markov decision processes
    • MUNDHENK, M., GOLDSMITH, J., AND ALLENDER, E. 1997. The complexity of the policy existence problem for partially-observable finite-horizon Markov decision processes. In Proceedings of the 25th Mathematical Foundations of Computer Sciences. Lecture Notes in Computer Science, vol. 1295: Springer-Verlag, New York, pp. 129-138.
    • (1997) In Proceedings of the , vol.25 , pp. 129-138
    • Mundhenk, M.1    Goldsmith, J.2    Allender, E.3
  • 66
    • 0041448596 scopus 로고    scopus 로고
    • The decision-theoretic interactive video advisor
    • NGUYEN, H., AND HADDAWY, P. 1999. The decision-theoretic interactive video advisor. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Nguyen, H.1    Haddawy, P.2
  • 69
    • 0000977910 scopus 로고
    • The complexity of Markov decision processes
    • PAPADIMITRIOU, C., AND TSITSIKLIS, J. 1987. The complexity of Markov decision processes. Math. Oper. Res. 12, 3, 441-450.
    • (1987) Math. Oper. Res. , vol.12 , pp. 441-450
    • Papadimitriou, C.1    Tsitsiklis, J.2
  • 70
    • 0022913920 scopus 로고
    • A note on succinct representations of graphs
    • PAPADIMITRIOU, C., AND YANNAKAKIS, M. 1986. A note on succinct representations of graphs. Inf. Cont. 71, 181-185.
    • (1986) Inf. Cont. , vol.71 , pp. 181-185
    • Papadimitriou, C.1    Yannakakis, M.2
  • 71
    • 0002475804 scopus 로고
    • Approximating optimal policies for partially observable stochastic domains
    • PARR, R., AND RUSSELL, S. 1995. Approximating optimal policies for partially observable stochastic domains. In Proceedings of IJCAI-95.
    • (1995) In Proceedings of IJCAI , pp. 95
    • Parr, R.1    Russell, S.2
  • 72
  • 74
    • 0004611825 scopus 로고    scopus 로고
    • Bayesian networks for dependability analysis: An application to digital control reliability
    • PORTINALE, L., AND BoBBio, A. 1999. Bayesian networks for dependability analysis: an application to digital control reliability. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Portinale, L.1    Bobbio, A.2
  • 76
    • 0442293992 scopus 로고    scopus 로고
    • Integration of Partially Observable Markov Decision Processes and Reinforcement Learning for Simulated Robot Navigation
    • PYEATT, L. 1999. Integration of Partially Observable Markov Decision Processes and Reinforcement Learning for Simulated Robot Navigation. Ph.D. dissertation. Colorado State Univ.
    • (1999) Ph.D. Dissertation. Colorado State Univ.
    • Pyeatt, L.1
  • 77
    • 33749197074 scopus 로고    scopus 로고
    • Learning hidden Markov models with geometrical constraints
    • SIIATKAY, H. 1999. Learning hidden Markov models with geometrical constraints. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Siiatkay, H.1
  • 78
    • 0000375787 scopus 로고
    • Probabilistic robot navigation in partially observable environments
    • SIMMONS, R., AND KOENIG, S. 1995. Probabilistic robot navigation in partially observable environments. In Proceedings of IJCAI-95.
    • (1995) In Proceedings of IJCAI , pp. 95
    • Simmons, R.1    Koenig, S.2
  • 79
    • 0015658957 scopus 로고
    • The optimal control of partially observed Markov processes over the finite horizon
    • SMALLWOOD, R., AND SONDIK, E. 1973. The optimal control of partially observed Markov processes over the finite horizon. Oper. Res. 21, 1071-1088.
    • (1973) Oper. Res. , vol.21 , pp. 1071-1088
    • Smallwood, R.1    Sondik, E.2
  • 81
    • 0001060347 scopus 로고
    • Sufficient statistics in the optimal control of stochastic systems
    • STREIBEL, C. 1965. Sufficient statistics in the optimal control of stochastic systems. J. Math. Anal. Appl. 12, 576-592.
    • (1965) J. Math. Anal. Appl. , vol.12 , pp. 576-592
    • Streibel, C.1
  • 83
    • 0026239342 scopus 로고
    • PP is as hard as the polynomial-time hierarchy
    • TODA, S. 1991. PP is as hard as the polynomial-time hierarchy. SIAM J. Comput. 20, 865-877.
    • (1991) SIAM J. Comput. , vol.20 , pp. 865-877
    • Toda, S.1
  • 84
    • 0000027812 scopus 로고
    • Complexity classes defined by counting quantifiers
    • TORâN, J. 1991. Complexity classes defined by counting quantifiers. J. ACM 38, 3, 753-774.
    • (1991) J. ACM , vol.38 , pp. 753-774
    • Torân, J.1
  • 85
    • 0025491302 scopus 로고
    • Solving /j-horizon, stationary Markov decision problems in time proportional to log h
    • TSENG, P. 1990. Solving /j-horizon, stationary Markov decision problems in time proportional to log h. Oper. Res. Lett. 9, 5 (Sept.), 287-297.
    • (1990) Oper. Res. Lett. , vol.9 , pp. 287-297
    • Tseng, P.1
  • 86
    • 0003114481 scopus 로고    scopus 로고
    • How to elicit many probabilities
    • VAN DER GAAG, L., RENOOIJ, S., WITTEMAN, C, ALEMAN, B., AND TALL, B. 1999. How to elicit many probabilities. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif., pp. 647-654.
    • (1999) In Proceedings of the , vol.15 , pp. 647-654
    • Van Der Gaag, L.1    Renooij, S.2    Tall, B.3
  • 87
    • 0026375502 scopus 로고
    • Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits
    • VINAY, V. 1991. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Proceedings of the 6th Structure in Complexity Theory Conference. IEEE Computer Society Press, Los Alamitos, Calif., pp. 270-284.
    • (1991) In Proceedings of the , vol.6 , pp. 270-284
    • Vinay, V.1
  • 88
    • 0022733806 scopus 로고
    • The complexity of combinatorial problems with succinct input representation
    • WAGNER, K. 1986. The complexity of combinatorial problems with succinct input representation. Acta. Inf. 23, 325-356.
    • (1986) Acta. Inf. , vol.23 , pp. 325-356
    • Wagner, K.1
  • 89
    • 4243168488 scopus 로고    scopus 로고
    • A process control algorithm for concentrating mixed-waste based on Bayesian cg-networks
    • WELCH, R. L., AND SMOTH, C. 1999. A process control algorithm for concentrating mixed-waste based on Bayesian cg-networks. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif.
    • (1999) In Proceedings of the , vol.15
    • Welch, R.L.1    Smoth, C.2
  • 90
    • 34249925148 scopus 로고
    • Partially observed Markov decision processes: A survey
    • WHITE, C., III. 1991. Partially observed Markov decision processes: A survey. Ann. Oper. Res. 32, 215-230.
    • (1991) Ann. Oper. Res. , vol.32 , pp. 215-230
    • White, C.1
  • 91
    • 85016628903 scopus 로고    scopus 로고
    • A model approximation scheme for planning in partially observable stochastic domains
    • ZHANG, N., AND Liu, W. 1997. A model approximation scheme for planning in partially observable stochastic domains. J. Artif. Int. Res. 7, 199-230.
    • (1997) J. Artif. Int. Res. , vol.7 , pp. 199-230
    • Zhang, N.1    Liu, W.2
  • 92
    • 0000675435 scopus 로고    scopus 로고
    • A method for speeding up value iteration in partially observable Markov decision processes
    • ZHANG, N. L., LEE, S. S., AND ZHANG, W. 1999. A method for speeding up value iteration in partially observable Markov decision processes. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence. Morgan-Kaufman, San Francisco, Calif., pp. 696-703.
    • (1999) In Proceedings of the , vol.15 , pp. 696-703
    • Zhang, N.L.1    Lee, S.S.2    Zhang, W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.