M. L. Litmman, S. M. Majercik, and T. Pitassi. Stochastic boolean satisfiability. Journal of Automated Reasoning, 27(3):251--296, 2001. Home/Search Document Details and Download
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Scenario-based Stochastic Constraint Programming - Suresh Manandhar And (Correct)
....difference is that stochastic constraint programs by using a scenario based interpretation can immediately call upon complex and powerful constraint propagation techniques. Stochastic constraint programming was inspired by both stochastic integer programming and stochastic satisfiability [Littman et al. 2000] . It is designed to take advantage of some of the best features of each framework. For example, we are able to write expressive models using non linear and global constraints, and to exploit efficient constraint propagation algorithms. In operations research, scenarios are used in stochastic ....
M. L. Littman, S. M. Majercik, and T. Pitassi. Stochastic boolean satisfiability. Journal of Automated Reasoning, 2000.
Phase Transitions of PP-Complete Satisfiability Problems - Bailey, Dalmau, Kolaitis (Correct)
....closely related to QSAT is stochastic Boolean satisfiability SSAT, which is the problem of evaluating an expression consisting of existential and ranodmized quantifiers applied to a Boolean formula. Experimental results on phase transitions for SSAT have been reported in [Littman, 1999] and [Littman et al. 2001] . Between NP and PSPACE lie several other important complexity classes that contain problems of significance in artificial intelligence. Two such classes, closely related to each other and of interest to us here, are #P and PP. The class #P, introduced and first studied by [V aliant, 1979a; ....
....carried out to study the median running time of an extension of the DPLL procedure on instances ( i) of the PP complete decision problem #SAT in which was a random 3CNF formula drawn from F 3 (n; rn) and i = 2 t , for some nonnegative integer t n. These experiments were also reported in [Littman et al. 2001] , which additionally contains a discussion on possible phase transitions for the decision problem #SAT and preliminary results concerning coarse upper and lower bounds for the critical ratios at which phase transitions may occur (in these two papers #SAT is called MAJSAT) As noted earlier, the ....
[Article contains additional citation context not shown here]
M.L. Littman, S.M. Majercik, and T. Pitassi. Stochastic Boolean satisfiability. Journal of Automated Reasoning, 2001. To appear.
Stochastic Constraint Programming - Walsh (2000) (6 citations) (Correct)
....If the optimal satisfaction is h or more, BT returns a value greater than or equal to h . If the optimal satisfaction is l or less, BT returns a value less than or equal to l . S is the set of stochastic variables. As in the Davis Putnam like algorithm for stochastic satisfiability (Littman, Majercik, Pitassi 2000), upper and lower bounds, h and l are used to prune search. By setting l = h = we can determine if the optimal satisfaction is at least . Alternatively, by setting l = 0 and h = 1, we can determine the optimal satisfaction. The calculation of upper and lower bounds in recursive ....
....could be useful to model the power output of the power stations that we decide to operate. Interval reasoning techniques could be extended to deal with such variables. Related work Stochastic constraint programming is inspired by both stochastic integer programming and stochastic satisfiability (Littman, Majercik, Pitassi 2000). It shares the advantages that constraint programming has over integer programming (e.g. global constraints, non linear constraints, and constraint propagation) It also shares the advantages that constraint programming has over satisfiability (e.g. global constraints, and arithmetic ....
Littman, M.; Majercik, S.; and Pitassi, T. 2000. Stochastic Boolean satisfiability. Journal of Automated Reasoning.
Stochastic Constraint Programming - Walsh (2000) (6 citations) (Correct)
....If the optimal satisfaction is or more, BT returns a value greater than or equal to . If the optimal satisfaction is or less, BT returns a value less than or equal to . N is the set of stochastic variables. As in the Davis Putnam like algorithm for stochastic satisfiability (Littman, Majercik, Pitassi 2000), upper and lower bounds, and are used to prune search. By setting 9 9 , we can determine if the optimal satisfaction is at least . Alternatively, by setting g9 and .9 , we can determine the optimal satisfaction. The calculation of upper and lower bounds in recursive calls requires ....
....could be useful to model the power output of the power stations that we decide to operate. Interval reasoning techniques could be extended to deal with such variables. Related work Stochastic constraint programming is inspired by both stochastic integer programming and stochastic satisfiability (Littman, Majercik, Pitassi 2000). It shares the advantages that constraint programming has over integer programming (e.g. global constraints, non linear constraints, and constraint propagation) It also shares the advantages that constraint programming has over satisfiability (e.g. global constraints, and arithmetic ....
Littman, M.; Majercik, S.; and Pitassi, T. 2000. Stochastic Boolean satisfiability. Journal of Automated Reasoning.
Initial Experiments in Stochastic Satisfiability - Littman (1999) (5 citations) Self-citation (Littman) (Correct)
....for its evidence nodes, and the value for a query node, what is the probability that the query node takes on the given value given the evidence is #P complete (Roth 1996) Any belief network (with rational conditional probability tables) can be represented as a Boolean formulae. The reduction (Littman, Majercik, Pitassi 1999) essentially consists of creating one variable per node in the belief network and one per conditional probability table entry. Clauses in the formula select a value for each belief network node depending on its parents values. From this, it follows that the belief network inference decision ....
.... NP PP PSPACE, we might expect Sat Majsat E Majsat SSat in terms of peak work. In fact, the experiments come out with Sat E Majsat SSat Majsat. That is, Majsat comes out as the hardest instead of the second easiest. This pattern can be observed with a range of values of n and k (Littman, Majercik, Pitassi 1999). The facts that E Majsat is easier than Majsat and that Sat is easier than SSat probably stem from the fact that randomized quantifiers are harder to prune than are existential quantifiers. SSat and E Majsat (c = n=2) both consist of half existential and half randomized quantifiers, and have ....
[Article contains additional citation context not shown here]
Littman, M. L.; Majercik, S. M.; and Pitassi, T. 1999. Stochastic Boolean satisfiability. Submitted.
MAP Complexity Results and Approximation Methods - James Park Computer (2002) (3 citations) (Correct)
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M. L. Litmman, S. M. Majercik, and T. Pitassi. Stochastic boolean satisfiability. Journal of Automated Reasoning, 27(3):251--296, 2001.
Stochastic Constraint Programming - Walsh (2001) (6 citations) (Correct)
No context found.
M.L. Littman, S.M. Majercik, and T. Pitassi. Stochastic Boolean satisfiability. Journal of Automated Reasoning, 2000.
Stochastic Constraint Programming - Toby Walsh Department (2001) (6 citations) (Correct)
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M.L. Littman, S.M. Majercik, and T. Pitassi. Stochastic Boolean satisfiability. Journal of Automated Reasoning, 2000.
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