• Journal of KIISE:Software and Applications
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• v.34 no.7
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• pp.616-624
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• 2007

Sudoku can be regarded as a SAT problem. Various encodings are known for encoding Sudoku as a Conjunctive Normal Form (CNF) formula, which is the standard input for most SAT solvers. Using these encodings for large Sudoku, however, generates too many clauses, which impede the performance of state-of-the-art SAT solvers. This paper presents an optimized CNF encodings of Sudoku to deal with large instances of the puzzle. We use fixed cells in Sudoku to remove redundant clauses during the encoding phase. This results in reducing the number of clauses and a significant speedup in the SAT solving time.

• Journal of KIISE:Software and Applications
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• v.31 no.11
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• pp.1560-1567
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• 2004

In temporal logic model checking, the number of states is exponentially increased by the size of a model. This is called the state explosion problem. Abstraction, partial order, symmetric, etc. are widely used to avoid the problem. They reduce a number of states by exploiting structural information in a model. Instead, this paper proposes the relay model checking that decomposes a temporal formula to be verified into several sub-formulas and then model checking them one by one. As a result, we solve complex games that can't handle with previous techniques.

• Journal of Korea Game Society
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• v.4 no.1
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• pp.58-66
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• 2004

This paper uses counterexamples for solving reachability games. An objective. of the game we consider here is to find out a minimal path from an initial state to the goal state. We represent initial states and game rules as finite state model and the goal state as temporal logic formula. Then, model checking is used to determine whether the model satisfies the formula. In case the model does not satisfy the formula, model checking generates a counterexample that shows how to reach the goal state from an initial state. In this way, we solve many of small-sized Push Push games. However, we cannot handle larger-sized games due to the state explosion problem. To mitigate the problem, abstraction is used to reduce the state space to be che cked. As a result, unsolved games are solved with the abstraction technique we propose inthis paper.

• The KIPS Transactions:PartD
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• v.11D no.6
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• pp.1295-1300
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• 2004

Although model checking has gained its popularity as one of the most effective approaches to the formal verification, it has to deal with the state explosion problem to be widely used in industry. In order to mitigate the problem, this paper proposes an ion technique to obtain a reduced model M' from a given original model M. Our technique Identifies the set of necessary variables for model checking and projects the state space onto them. The model M' is smaller in both size and behavior than the original model M, written M'$\leq$M. Since the result of reachability analysis with M' is preserved in M, we can do reachability analysis with model checking using M' instead of M. The abstraction technique is applied to Push Push games, and two model checkers - Cadence SMV and NuSMV - are used to solve the games. As a result, most of unsolved games with the usual model checking are solved with the ion technique. In addition, ion shows that there is much of time and space improvement. With Cadence SMV, there is 87% time improvement and 79% space one. And there is 83% time improvement and 56% space one with NuSMV.

• Korean Journal of Social Welfare
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• v.50
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• pp.61-85
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• 2002

Using the 2001 Family Income and Expenditure Survey micro-data, this study analyses the anti-poverty effectiveness of public and private income transfers. In this study, the anti-poverty effectiveness of income transfers is summarized in two ways; 1) the poverty reduction effect of the income transfers, and 2) the poverty reduction efficiency of the income transfers. The poverty reduction effects are measured with several poverty indices including the head-count ratio, poverty gap, and Sen index. Using Beckerman's model, this study also analyses the poverty reduction efficiency of income transfers. This analysis documents substantial differences in the anti-poverty effectiveness of public and private income transfers. Although the private income transfers contribute more to reduce the head-count poverty ratio and Sen index than public income transfers, their differences are significantly reduced after the enactment of National Basic Livelihood Security Act. The results also reveal that the anti-poverty effectiveness of public and private income transfers vary by the types of families. In families headed by elderly and working aged, private income transfers have more anti-poverty effectiveness. But, public income transfers contribute more to reduce poverty than private income transfers among families headed by single adults with children. The results of this study suggest that recent changes in anti-poverty policies in Korea have been strengthened the Government's responsibility. And more importantly, to effectively reduce poverty among the poor families, anti-poverty polices must be designed to consider different family types.